Find polynomial s(n) such that s(n)=∑... (refer to description)

Question

Find polynomial s(n) such that s(n)=∑ⁿ_i=1(i²−i) 

Then prove that your polynomial is equal to the sum for all n∈Z⁺

Answer 1

I've recorded and uploaded a video solution here:

https://www.youtube.com/watch?v=Mk_mSSaOF1Q

Here is a visual proof.

https://www.desmos.com/calculator/fpetnwtufr