HMMT November 2021 T3

Suppose $m$ and $n$ are positive integers for which

• the sum of the first $m$ multiples of $n$ is 120 , and
• the sum of the first $m^{3}$ multiples of $n^{3}$ is 4032000 .

Determine the sum of the first $m^{2}$ multiples of $n^{2}$.