  The energy density is calculated in coordinate space for $^{12}$C, $^{40}$Ca,
$^{48}$Ca, and $^{208}$Pb using a dispersive optical model constrained by all
relevant data including the corresponding energy of the ground state. The
energy density of $^{8}$Be is also calculated using the Green's function
Monte-Carlo method employing the Argonne/Urbana two and three-body
interactions. The nuclear interior minimally contributes to the total binding
energy due to the 4$\pi r^2$ phase space factor. Thus, the volume contribution
to the energy in the interior is not well constrained. The
dispersive-optical-model energy densities are in good agreement with \textit{ab
initio} self-consistent Green's function calculations of infinite nuclear
matter restricted to treat only short-range and tensor correlations. These
results call into question the degree to which the equation of state for
nuclear matter is constrained by the empirical mass formula. In particular, the
results in this paper indicate that saturated nuclear matter does not require
the canonical value of 16 MeV binding per particle but only about 13-14 MeV
when the interior of $^{208}$Pb is considered.
