Here are some quotes from past mormon leaders
Brigham Young (Second President); “Why are so many of the inhabitants of the earth cursed with a sin of blackness? It comes in consequence of their fathers rejecting the power of the Holy Priesthood, and the law of God. They will go down to death. And when all the rest of the children have received their blessings in the Holy Priesthood, then that curse will be removed from the seed of Cain, and they will then come up and possess the priesthood, and receive all the blessings which we now are entitled to. The volition of the creature is free; this is a law of their existence, and the Lord cannot violate his own law; were he to do that, he would cease to be God” (August 19, 1866, Journal of Discourses 11:272)
Brigham Young; “Shall I tell you the law of God in regard to the African race? If the white man who belongs to the chosen seed mixes his blood with the seed of Cain, the penalty, under the law of God, is death on the spot. This will always be so.” (Brigham Young, March 8, 1863: a conference talk in the Tabernacle, Journal of Discourses 10:110).
Brigham Young; “Now then, in the kingdom of God on the earth, a man who has the African blood in him cannot hold one jot nor tittle of Priesthood; Why? Because they are the true eternal principals the Lord Almighty has ordained, and who can help it −; men cannot, the angels cannot, and all the powers of Earth and Hell cannot take it off, but thus saith the Eternal, ‘I am, what I am, I take it off at My pleasure’, and not one particle of power can that posterity of Cain have, until the time comes the [Lord] says He will have it taken away. That time will come, when they will have the privilege of all we have the privilege of, and more. In the Kingdom of God on the Earth the Africans cannot hold one particle of power in Government” (Vol. 3 1852-1854, Fred C. Collier, ed., p. 43. Speech given to the Joint Session of the Legislature in Salt Lake City, on Thursday, February 5, 1852. Brackets in original).
Brigham Young; “How long is that race to endure the dreadful curse that is upon them? That curse will remain upon them, and they never can hold the Priesthood or share in it until all the other descendants of Adam have received the promises and enjoyed the blessings of the Priesthood and the keys thereof. Until the last ones of the residue of Adam's children are brought up to that favourable position, the children of Cain cannot receive the first ordinances of the Priesthood. They were the first that were cursed, and they will be the last from whom the curse will be removed. When the residue of the family of Adam come up and receive their blessings, then the curse will be removed from the seed of Cain, and they will receive blessings in like proportion” (Brigham Young, October 9, 1859, Journal of Discourses 7:290-291).
John Taylor (Third President); “And after the flood we are told that the curse that had been pronounced upon Cain was continued through Ham’s wife, as he had married a wife of that seed. And why did it pass through the flood? Because it was necessary that the devil should have a representation upon the earth as well as God” (John Taylor, August 28th, 1881, Journal of Discourses 22:304. See also Latter-day Prophets Speak: Selections from the Sermons and Writings of Church Presidents, p.157, Daniel H. Ludlow, ed.). (B. 1808; D. 1887)
John Taylor; “Why is it, in fact, that we should have a devil? Why did not the Lord kill him long ago? Because he could not do without him. He needed the devil and a great many of those who do his bidding just to keep men straight, that we may learn to place our dependence upon God, and trust in Him, and to observe his laws and keep his commandments. When he destroyed the inhabitants of the antediluvian world, he suffered a descendant of Cain to come through the flood in order that he might be properly represented upon the earth” (John Taylor, October 29, 1882, Journal of Discourses 23:336).
David O. McKay (Ninth Mormon President); "I know of no scriptural basis for denying the Priesthood to Negroes other than one verse in the Book of Abraham (1:26); however, I believe, as you suggest, that the real reason dates back to our pre-existent life.” (Letter dated November 3, 1947)
Joseph Fielding Smith (Tenth President); “That the negro race, for instance, have been placed under restrictions because of their attitude in the world of spirits, few will doubt. It cannot be looked upon as just that they should be deprived of the power of the Priesthood without it being a punishment for some act, or acts, performed before they were born. Yet, like all other spirits who come into this world, they come innocent before God so far as mortal existence is concerned, and here, under certain restrictions, they may work out their second estate. If they prove faithful in this estate, without doubt, our Eternal Father, who is just and true, will reward them accordingly and there will be in store for them some blessings of exaltation” (The Way To Perfection, p.43; Smith the tenth president of the Mormon Church until 1972, the son of Joseph F. Smith, the sixth president. Founder Joseph Smith, Jr., was Joseph Fielding's great-uncle.
Joseph Fielding Smith; “There is a reason why one man is born black and with other disadvantages, while another is born white with great advantages. The reason is that we once had an estate before we came here, and were obedient; more or less, to the laws that were given us there. Those who were faithful in all things there received greater blessings here, and those who were not faithful received less” (Doctrines of Salvation 1:61. Italics in original).
Joseph Fielding Smith; “NO NEUTRALS IN HEAVEN. There were no neutrals in the war in heaven. All took sides either with Christ or with Satan. Every man had his agency there, and men receive rewards here based upon their actions there, just as they will receive rewards hereafter for deeds done in the body. The Negro, evidently, is receiving the reward he merits”(Doctrines of Salvation 1:65-66. Italics in original)
Joseph Fielding Smith; “Not only was Cain called upon to suffer, but because of his wickedness he became the father of an inferior race. A curse was placed upon him and that curse has been continued through his lineage and must do so while time endures. Millions of souls have come into this world cursed with a black skin and have been denied the privilege of Priesthood and the fullness of the blessings of the Gospel. These are the descendants of Cain. Moreover, they have been made to feel their inferiority and have been separated from the rest of mankind from the beginning” (Joseph Fielding Smith, The Way to Perfection, p.101).
Joseph Fielding Smith; “The Latter-day Saints, so commonly called ‘Mormons,’ have no animosity towards the Negro, Neither have they described him as belonging to an ‘inferior race’” (Joseph Fielding Smith, Answers to Gospel Questions 4:170).
Joseph Fielding Smith; "Since Cain slew his brother Abel in order to obtain all the rights of priesthood to descend through his lineage, the Lord decreed that the children of Cain should not have the privilege of bearing the priesthood until Abel had posterity who could have the priesthood and that will have to be in the far distant future. When this is accomplished on some other world, then the restrictions will be removed from the children of Cain who have been true in this ‘second’ estate” (Joseph Fielding Smith, Answers to Gospel Questions 2:188).
Harold B. Lee (Eleventh President); “There is no truth more plainly taught in the Gospel than that our condition in the next world will depend upon the kind of lives we live here. ‘All that are in the graves shall hear his voice, and shall come forth; they that have done evil, unto the resurrection of damnation.’ (John 5:28-29.) Is it not just as reasonable to suppose that the conditions in which we now live have been determined by the kind of lives we lived in the pre-existent world of spirits? That the apostles understood this principle is indicated by their question to the Master when the man who was blind from his birth was healed of his blindness, ‘Master, who did sin, this man or his parents that he was born blind?’ (John 9:2.) Now perhaps you will have a partial answer to some of your questions as to why, if God is a just Father, that some of his children are born of an enlightened race and in a time when the Gospel is upon the earth, while others are born of a heathen parentage in a benighted, backward country; and still others are born to parents who have the mark of a black skin with which the seed of Cain were cursed and whose descendants were to be denied the rights of the priesthood of God” (Decisions for Successful Living, pp.164-165). Lee was the 11th President of the Church until 1973.
Ezra Taft Benson (Thirteenth President); “The arm of flesh may not approve nor understand why God has not bestowed the priesthood on women or the seed of Cain, but God's ways are not man's ways” (Ezra Taft Benson, Conference Reports, October 1967, p.34).
Apostle Melvin J. Ballard; “Why is it in this Church we do not grant the priesthood to the Negroes? It is alleged that the Prophet Joseph said--and I have no reason to dispute it--that it is because of some act committed by them before they came into this life. It is alleged that they were neutral, standing neither for Christ nor the devil. But, I am convinced it is because of some things they did before they came into this life that they have been denied the privilege. The races of today are very largely reaping the consequences of a previous life” (Sermons and Missionary Service of [Apostle] Melvin J. Ballard, p.248). (B.1873; D. 1939) Melvin J. Ballard is the grandfather of M. Russell Ballard who currently serves as a Mormon apostle.
Apostle George F. Richards; “The Negro race have been forbidden the priesthood, and the higher temple blessings, presumably because of their not having been valiant while in the spirit. It does not pay to be anything but valiant” (Apostle George F. Richards, Conference Reports, October 1947, p.57).( B.1861; D. 1950)
Alvin R. Dyer; “The reason that spirits are born into Negro bodies is because those spirits rejected the priesthood of God in the Pre-existence. This is the reason why you have Negroes on the earth. …All of this is according to a well worked-out plan, that these millions and billions of spirits awaiting birth in the pre-existence would be born through a channel or race of people. Consequently, the cursed were to be born through Ham. . . . This is why you have colored people, why you have dark people and why you have white people” (Alvin R. Dyer (at the time was an Assistant to the Twelve, later to be 1st Presidency under McKay); “For What Purpose?” March 18, 1961)
Mark E. Petersen; “We cannot escape the conclusion that because of performance in the pre-existence some of us are born as Chinese, some as Japanese, some as Indians, some as Negroes, some as Americans, some as Latter-day Saints. These are rewards and punishments, fully in harmony with His established policy in dealing with sinners and saints, rewarding all according to their deeds” (Mark E. Petersen, “Race Problems – as they affect the church,” August 27, 1954, p.11). (B.1900; D. 1984) Member of the Quorum of the Twelve Apostles of The Church of Jesus Christ of Latter-day Saints from 1944-1984. Managing editor of the Church-owned Deseret News in 1935 and editor in 1941.
Apostle Mark Petersen; “In spite of all he did in the pre-existent life, the Lord is willing, if the Negro accepts the gospel with real, sincere faith, and is really converted, to give him the blessings of baptism and the gift of the Holy Ghost. If that Negro is faithful all his days, he can and will enter the celestial kingdom. He will go there as a servant, but he will get a celestial resurrection. He will get a place in the celestial glory. He will not go then with even the honorable men of the earth to the terrestrial glory, nor with the ones spoken of as being without law.” (Mark E. Petersen, “Race Problems – as they affect the church,” August 27, 1954, p.17).