  In this paper we compute the sum of the $k$-th powers over any finite
commutative unital rings, thus generalizing known results for finite fields,
the rings of integers modulo $n$ or the ring of Gaussian integers modulo $n$.
As an application we focus on quotient rings of the form
$\mathbb{Z}/n\mathbb{Z}[x]/(f(x))$ for any polynomial $f\in\mathbb{Z}[x]$
