Let $u$ be a harmonic function on $\mathbb R^n$. We know that if $B$ is a ball centered at $x$, then
$u(x) = \frac{1}{|B|} \int_B u(y) dy = \frac{1}{|\partial B|} \int_{\partial B} u(z) dS(z).$
I am wondering if there is an analagous result with the ball $B$ replaced by a different set, perhaps an $n$-cube or an ellipsoid. Is such a generalize mean value formula possible?