algebra precalculus - Sum of series: $1*3*(2^2) + 2*4*(3^2) + 3*5*(4^2) + dots$?

I am trying to find the sum of the above series.

The sum till n terms can be found using power series expansion. However, I'm trying to solve this using the method of difference (a.k.a. Telescoping sum or $V_n$ method).

In this method, the general term is expressed as the difference between two consecutive values of some function. Like the following:

$T_n = V_n - V_{n-1}$

and then the sum is taken which comes to be

$S_n = V_n - V_0$

The general term of the series in question can be represented as a product:

$T_n = n(n+1)^2(n+2)$

But I am unable to represent this as a difference. How can I proceed from here to find the sum?