Consider two GPs $2, 2^2, 2^3, \ldots$ and $4, 4^2, 4^3, \ldots$ of $60$ and $n$ terms respectively. If the geometric mean of all the $60+n$ terms is $2^{q}$ for some integer $q$, then $\sum_{k=1}^{n} k(n-k)$ is equal to