Solve $x_{n+1}=2x_n-n^3$

Question

I want to solve this difference equation, using the z-transforms.

Using a table I get that:

$x_{n+1}\rightarrow zX(z)$

$2x_n\rightarrow 2X(z)$

but then I cannot find any entry for $-n^3$. Using WA this transform is meant to be

$-\frac{(z (1 + 4 z + z^2))}{(-1 + z)^4}$

But how is this found using a table? I thought of using the definition

$\sum_0^\infty -\frac{n^3}{z^k}$, but I am not sure how this turns into the WA result.

Any ideas?

Thanks