The question:
Find the sum of the first $n$ terms of $\sum^n_{k=1}k^3$ [Hint: consider $(k+1)^4-k^4$]
[Answer: $\frac{1}{4}n^2(n+1)^2$]
My solution:
$\begin{align} \sum^n_{k=1}k^3&=1^3+2^3+3^3+4^3+\cdots+(n-1)^3+n^3\\ &=\frac{n}{2}[\text{first term} + \text{last term}]\\ &=\frac{n(1^3+n^3)}{2} \end{align}$
What am I doing wrong?