So the title may be a little bit vague, but I am quite stuck with the following problem.
Asked is to first prove that $(k + 1)^3 - k^3 = 3k^2 + 3k + 1$. This is not the problem however. The question now asks to prove that

$$ \sum\_{k=1}^{n} k^2 = \frac{1}{6}n(n+1)(2n+1)$$ using the fact that $(k + 1)^3 - k^3 = 3k^2 + 3k + 1$. I have no idea however to start working on this. Anyone have any idea? Does this have anything to do with telescopic series?