This is my first proof using induction and, as expected, I'm stuck. In fact, I don't know where to start. Any help is appreciated. THanks.
Start with the base case, when $\displaystyle n=1$ is it true?
Then the induction step is to assume it true for $\displaystyle n=k$, and show that implies that it is true when $\displaystyle n=k+1$.
So you need to show that the assumption that:
$\displaystyle \sum_{i=1}^ki^3=\left(\frac{k(k+1)}{2} \right)^2$
implies that:
$\displaystyle \sum_{i=1}^{k+1}i^3 = \left(\sum_{i=1}^ki^3\right) + (k+1)^3=\left(\frac{(k+1)(k+2)}{2} \right)^2$
CB