You aren't sure if n(n + 1)(4n - 1)/6 is right?? Well, it's correct.

I'd do it inductively. Your base case is n = 1 and it works just fine.

So assume that for some value of k.

Then you need to show that

So. I'll give you an outline, let's see what you can do with it. You need to show that

How many terms do you need to add to the k case on the RHS to make it equal to the k + 1 case?

-Dan