Relation between Hochschild cohomologoy $HH^{n}(\mathbb{Z}[G], M)$ and the cohomology group $H^{n}(G,M)$ for $G$ a cyclic group

Question

Let $G$ be an infinite cyclic group and $M$ an abelian group with $\mathbb{Z}[G]-$bimodule structure. Fix an integer $n\in\mathbb{N}$. Is there a relation between the Hochschild's cohomology group $HH^{n}(\mathbb{Z}[G],M)$ and the cohomology group $H^{n}(G,M)$?...Are these two isomorphic groups ?