1. The problem statement, all variables and given/known data I have the series 1^3+2^3+3^3......n^3, and need to find a formula containing n to represent the sum of the nth terms. The motivation is to find a conjecture, which I can then prove using mathematical induction. 3. The attempt at a solution I see that n=1 , 1^3=1 n=2 , 1^3+2^3=9 n=3, 1^3+2^3+3^3=36 n=4, sum=100 n=5 sum = 225. But I cannot come up with a formula to represent the sums. I think this is calculus II series material, but I'm not sure where to start. Could someone point me in the right direction? I used a computer to arrive at 1^3+2^3+3^3......n^3=(1/4)*n^2*(n+1)^2 but do not understand how to get there myself.