Question: Prove 1^3 + 2^3 + ... + n^3 = (1 + 2 + ... n)^2
The basis step is satisfied but the induction step is troubling me. So I assume P(k) is true where P(k) is 1^3 + 2^3 + ... + k^3 = (1 + 2 + ... k)^2 and I want to show that P(k + 1) holds as well but I have no idea how to even begin the proof.
Can anyone provide a hint for me as to how I should start? Thanks in advance.