If $\gcd(a, b) = p$, where $p$ is a prime. Then what are possible values of $\gcd(a^3, b^2)$?

I have already calculated that $\gcd(a^2, b^2) = p^2$. $\gcd(a^2, b) = p$ or $p^2$, $\gcd(a^3, b) = p$ or $p^2$ or $p^3$. Can anybody give me any idea? how will I find the possible value of $\gcd(a^3, b^2)$?