The group cohomology of cyclic groups can be computed easily due to the periodity. Now how can one compute the group cohomology $H^r(\mathbb{Z}/n\mathbb{Z}\times \mathbb{Z}/n\mathbb{Z},M)$? As least in some special case, e.g. $M$ has trivial action, or even $M=\mathbb{Z}$?

Furthermore, can one compute $H^r(\mathbb{Z}/n\mathbb{Z}\times\cdots\times \mathbb{Z}/n\mathbb{Z},M)$?

The group cohomology of cyclic groups can be computed easily due to the periodity. Now how can one compute the group cohomology $H^r(\mathbb{Z}/n\mathbb{Z}\times \mathbb{Z}/n\mathbb{Z},M)$? As least in some special case, e.g. $M$ has trivial action, or even $M=\mathbb{Z}$? I would like to know the case that $M$ is not $\mathbb{Z}$.

Furthermore, can one compute $H^r(\mathbb{Z}/n\mathbb{Z}\times\cdots\times \mathbb{Z}/n\mathbb{Z},M)$?