  The neutron-proton Fermi-energy difference and the correlation to nucleon
separation energies for some magic nuclei are investigated with the Skyrme
energy density functionals and nuclear masses, with which the nuclear symmetry
energy at sub-saturation densities is constrained from 54 Skyrme parameter
sets. The extracted nuclear symmetry energy at sub-saturation density of 0.11
fm$^{-3}$ is 26.2 $\pm$ 1.0 MeV with 1.5 $\sigma$ uncertainty. By further
combining the neutron-skin thickness of 208Pb, ten Skyrme forces with slope
parameter of 28<L<65 are selected for the description of the symmetry energy
around saturation densities.
