I am looking for a proof of the following result: Let $\mathfrak{g}$ be a Lie algebra and $I$ an injective $\mathfrak{g}$-module. Then $\mathrm{H}^q(\mathfrak{g},I)=0$ $\forall q>0$. More precisely, I am looking for a proof in a textbook so that I can cite it.
The result shows up in Weibel's book (Exercise 2.5.1), but only as an exercise (no proof).