I knew that my mother was cheating on my father but I didn't tell my father to preserve and protect our family now am old and I want to know was it a sin that I didn't tell my father.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions. You did not inform us of the kind of cheating your mother had been practicing against your father. However, if she had been taking your father's money without her right then you had to exhort her to ask forgiveness from your father and give him back his rights. If she was committing adultery, you should have prevented her from that. If she gave up then you should cover her and should not inform anyone about that. If she did not give up committing adultery and insist on practicing it, in this case, you have to make all efforts to prevent her from that bad practice. If you cannot stop her then you should seek help of other relatives or those who can stop her from that sin. Letting her free on her way not making efforts to save her is an offence against her rather than a good act. Allah knows best.