sequences and series - An expression for the sum $sumlimits _{k=1}^{n-1} k , (n-k)^2$

I really don't know how to find the sum of the series:

$$\sum\limits _{k=1}^{n-1} k \, (n-k)^2 = 1(n-1)^2+2(n-2)^2+3(n-3)^2+\dots+(n-1)1^2.$$

My attempt:
I tried to approach the old school approach of how we find the sum of arithmetic-co geometric progression but unable to do so.

Any help is appreciated!