MEMO 2012 Problem 8

For any positive integer $n$ let $d(n)$ denote the number of positive divisors of $n$ . Do there exist positive integers $a$ and $b$ , such that $d(a)=d(b)$ and $d(a^2 ) = d(b^2 )$ , but $d(a^3 ) \ne d(b^3 )$ ?