Use Mathematical Induction to prove equation? Use mathematical induction to prove each of the following statements.
let $$g(n) = 1^3 + 2^3 + 3^3 + ... + n^3$$
Show that the function $$g(n)= \frac{n^2(n+1)^2}{4}$$ for all n in N
so the base case is just g(1) right? so the answer for the base case is 1, because 4/4 = 1
then for g(2) is it replace all of the n's with n + 1 and see if there is a concrete answer?

You want to show that $$\sum_{j=1}^n j^3 = \frac{n^2(n+1)^2}{4}.$$
You've shown that it holds for the base case, which is good.
Now, you assume that it holds for $n=k$:
$$\sum_{j=1}^k j^3 = \frac{k^2(k+1)^2}{4}.$$
Then, a strategy is to write out one part or the other for the $n=k+1$ case, and manipulate it so that you pull out the $n=k$ expression.  Let's do the sum:
$$\sum_{j=1}^{k+1} j^3 = \sum_{j=1}^{k} j^3 + (k+1)^3.$$
This is just algebra; I pulled out the last term and wrote it explicitly.  But now I can substitute in the assumption for the sum on the right hand side.
The rest is to manipulate the expression on the right hand side to come up with the expression
$$\frac{(k+1)^2(k+2)^2}{4},$$
and then you're done.
Can you take it from here?
