Why is mass a very concentrated form of energy? Does it have to do something with photons, phonons or nucleus?

Say I have a charge density $\rho(\vec{x})$ in some finite volume $V$, such that all of the multipole expansions apart from the monopole moment (meaning dipole, quadrupole and so forth) are zero. Does this mean that $\rho(\vec{x})$ is spherically symmetric? I know the opposite is true - meaning, ...