If $u$ is a solution to the equation $\triangle u +k^2 u=0$ in a 3D domain $\Omega$, then 
for any sphere which is contained in $\Omega$, we have
$$u(x)=\frac {p(R)}{4\pi R^2}\int_{|x-y|=R} u(y)dS_y,$$
where
$$p(R)=\frac{Rk}{\sin Rk}$$.

The formula and its derivation can be found in chapter IV of *Methods of Mathematical Physics* (Vol. 2)
by Courant and Hilbert.