  The symmetry energy coefficients in finite nuclei have been studied
systematically with a covariant density functional theory (DFT) and compared
with the values calculated using several available mass tables. Due to the
contamination of shell effect, the nuclear symmetry energy coefficients
extracted from the binding energies have large fluctuations around the nuclei
with double magic numbers. The size of this contamination is shown to be
smaller for the nuclei with larger isospin value. After subtracting the shell
effect with the Strutinsky method, the obtained nuclear symmetry energy
coefficients with different isospin values are shown to decrease smoothly with
the mass number $A$ and are subsequently fitted to the relation $\dfrac{4a_{\rm
sym}}{A}=\dfrac{b_v}{A}-\dfrac{b_s}{A^{4/3}}$. The resultant volume $b_v$ and
surface $b_s$ coefficients from axially deformed covariant DFT calculations are
$121.73$ and $197.98$ MeV respectively. The ratio $b_s/b_v=1.63$ is in good
agreement with the value derived from the previous calculations with the
non-relativistic Skyrme energy functionals. The coefficients $b_v$ and $b_s$
corresponding to several available mass tables are also extracted. It is shown
that there is a strong linear correlation between the volume $b_v$ and surface
$b_s$ coefficients and the ratios $b_s/b_v$ are in between $1.6-2.0$ for all
the cases.
