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.