Power series $\sum n^3a=?iso-8859-1?Q?=5Fnz^n$_=96_math.stackexchange.com?=

Power series $\sum n^3a_nz^n$ – math.stackexchange.com

If $f(z)=\sum a_nz^n$, what is $\sum n^3a_nz^n$? The desired sum is
$a_1z+8a_2z^2+27a_3z^3+\cdots$. I can't see how to write the desired sum
in terms of $f$. For example, I could substitute $kz$ …