1. The problem statement, all variables and given/known data Prove the following formulas by induction. (ii) 13+...+n3= (1+...+n)2. I am starting Spivak's Calculus by myself, and I simply do not understand Spivak's proof for the sum of the cubes equaling the square of the sum, exercise 1 (ii) of chapter 2 in his third edition. I tried to attach his proof to this thread. The only step I cannot figure out is the first, where (1+...+k+[k+1])2 = (1+...+k)2+2(1+...+k)(k+1)+(k+1)2. I have already worked through problem 1 (i), so I understand everything that follows the first line of the proof. But how/why does the square of the sums expand this way once induction is applied? Please help!