Inductive Proof on Well Known Sum
1. The problem statement, all variables and given/known data
Use induction to prove the equation
(1+2+...+n)^2 = 1^3 + 2^3 + ... + n^3
2. The attempt at a solution
I've done three inductive proofs previous to this one where I showed that the equation was true for some case (usually n=1), then assumed it was true for n, and proved it was true for n+1. This proof doesn't seem to fit that form though because for the other proofs I could write it as the right hand side of the equation (since it's assumed that it is true for n) plus the right hand side of the equation when n+1 is plugged in. But in this case..
(1+2+...+n+(n+1))^2 != (1+2+...+n)^2 + (n+1)^2
So, I guess I haven't done a proof like this and could use a nudge in the right direction..