For the Euclidean space $\mathbb{C}^n$ we have the flat metric:

It is a Kähler manifold: $\mathrm{d}(\omega)=\dfrac{\mathrm{i}}{2}\sum_{j}(\mathrm{d}^2 z_j\wedge\mathrm{d} \bar{z}_j-\mathrm{d} z_j\wedge\mathrm{d}^2 \bar{z}_j)=0$. Indeed the metric is described by a global Kähler potential:

Since the coefficients of the metric are constant, the other tensors, that always involve derivatives, vanish:

Therefore the flat metric $\mathbb{C}^n$ is Einstein of constant 0.