elementary number theory - Prove/disprove: if $a^2$ divides $b^3$, then $a$ divides $b$

Prove/disprove the following: if $a^2$ divides $b^3$, then $a$ divides $b$

I've tried rewriting as $b^3=a^2c$, but I can't seem to show anything else for $c$. If I can prove that it is/isn't an integer, that would prove the whole thing for me.