Given that

S(N)=

N

Σ...(2n-1)^3

n=1

Show that

S(N)=N^2(2N^2 - 1)

I tried expanding it and used the following formulas:

Σn=n(n+1)/2

Σn^2=n(n+1)(2n+1)/6

Σn^3=n^2(n+1)^2/4

But it doesn't give the answer.

I also tried substituting (2n-1) directly into the last formula but it also doesn't give the answer.

Please help,

Thanks