Some practice problems that I am stuck on, in my first week of this class.

Prove that 1^3+2^3...+n^3 = (1+2+...n)^2

Prove that 11^n+1 + 12^n+1 is divisible by 133

I can only show that these are true by using examples (i.e plugging stuff in). I don't know how to do the proof for either one.