Prove or reject: if $a^2|b^3$ then $a|b$

Question

I tried to find a counter example but failed!!
If $a^2|b^3$ then it is obvious that $a|b^3$ because $b^3=ka^2=(ka)a=k'a$ but we hardly can say $a|b$

Answer 1

Have you tried with $a=8$ and $b=12$?