How Did Three Sons Continue The Population?

Well, the very question is actually incorrect.  Sure, none would ever make the claim that the three sons(Seth, Cain, & Abel) didn't exist, but we mean that there were actually far more daughters and sons of Adam and Eve. We learn this fact in Genesis. "The days of Adam after he fathered Seth were 800 years; and he had other sons and daughters" (Genesis 5:4). The names were sadly never mentioned, but at the very least we do know the answer to this question!