Name for sums of the form $\sum_{n=0}^m n^p$?

Question

Is there a name for these sums?

$$\begin{align}\sum_{n=0}^m n^0 &= m \\[4pt] \sum_{n=0}^m n^1 &= \frac{m(m+1)}{2} \\[4pt] \sum_{n=0}^m n^2 &= \frac{m(m+1)(2m+1)}{6} \\[4pt] \sum_{n=0}^m n^3 &= \frac{m^2(m+1)(m+1)}{4} \end{align}$$

I've reached these results experimentally so there may be errors.

Answer 1

They're called power sums; see this MathWorld entry, for example.