  We investigate the symmetry energy in relation with the two-proton and
two-neutron separation energies using different nuclear mass data. For this
aim, we exploit the deformed relativistic Hartree-Bogoliubov theory in the
continuum (DRHBc), FRDM2012 and AME2020 data. First, we study the two-proton
and two-neutron separation energies in Pb and Ca isotopes by subtracting the
contribution of Coulomb energy. They show a strong correlation with neutron
number as well as with the neutron skin thickness. By taking the relative
difference of both separation energies, we derive the symmetry energy from Ca
and Pb isotopes. Since the nuclear surface contributes to the symmetry energy,
we deduce the volume symmetry energy by subtracting the surface contribution
using several mass models. The obtained symmetry energy coefficient, $a_{sym}$,
is 20.0 $\sim $ 22.7 MeV for Pb isotopes and 18.7 $\sim$ 19.3 MeV for Ca
isotopes from the DRHBc mass table data, while the results from other mass
tables are 19.6 $\sim$ 22.1 (20.7 $\sim$ 22.3) MeV for Pb isotopes and 18.9
$\sim$ 19.0 (19.6 $\sim$ 19.7) MeV for Ca isotopes from AME2020 (FRDM2012)
data. The volume contribution to the asymmetry coefficient, $a_{sym}^v$, which
depends on the ratio of the surface to the volume energy coefficients, $a_s /
a_v$, is also provided for each mass model. Since the ratio $a_s / a_v$ is
neither determined by nuclear theory, nor by experimental data, we have
investigated $a_{sym}^v$ by using the ratio $a_s / a_v$ as a free parameter,
and have obtained $a_{sym}^v = $ 27.0 MeV, almost irrespective of nuclear model
and isotopic chain, with the ratio $a_s / a_v$ constrained as $a_s / a_v = 1.10
\sim 1.13$.
