"And their sins and iniquities will I remember no more." (Hebrews 10: 17)
I remember reading a Christian author claim that God does not remember our sins anymore, but He does not forget them, either. Even today, there are men and women in the Body of Christ who still think that our sins are recorded somewhere.
What does the Bible say regarding our sins?:
"I, even I, am he that blotteth out thy transgressions for mine own sake, and will not remember thy sins." (Isaiah 43: 25)
How about this?
"As far as the east is from the west, so far hath he removed our transgressions from us." (Psalm 103: 12)
Before Jesus died on the Cross, He promised to send the Comforter, or our Advocate:
"8And when he is come, he will reprove the world of sin, and of righteousness, and of judgment: 9Of sin, because they believe not on me; 10Of righteousness, because I go to my Father, and ye see me no more; 11Of judgment, because the prince of this world is judged." (John 16: 8-11)
We are convicted of righteousness, because we now do believe on Him, we know that the rule of the world has been judged, and we recognize today that He is seated at the right hand of God the Father, justifying us (Romans 8: 31-34)
He does not forget out sins arbitrarily, but rather because someone else paid for all of them: His Son Jesus:
"13And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses; 14Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross; 15And having spoiled principalities and powers, he made a shew of them openly, triumphing over them in it." (Colossians 2: 13-15)
"But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin." (1 John 1: 7)
God remembers our sins no more because they have all been paid for, and paid for eternally.
John later writes:
"If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness." (1 John 1: 9)
God our Father is faithful to what Jesus did, and acting justly because His Son did a perfect work at the Cross.