Find Ordinary Generating Function for $k^3 (k \geq 2)$

Question

Could we find the OGF for the sequence $k^3, k \geq 2$?

Answer 1

A related problem

Apply the operator $(xD)^3= (xD)(xD)(xD) $ to $\frac{1}{1-x}$ gives your the answer.

Note:

$$D =\frac{d}{dx}. $$

Answer 2

Hint: $~k^3x^k=(x\frac{\partial}{\partial x})^3x^k$