  We determine the maximum number of copies of $K_{s,s}$ in a $C_{2s+2}$-free
$n$-vertex graph for all integers $s \ge 2$ and sufficiently large $n$.
Moreover, for $s\in\{2,3\}$ and any integer $n$ we obtain the maximum number of
cycles of length $2s$ in an $n$-vertex $C_{2s+2}$-free bipartite graph.
