  The entanglement properties of a class of topological stabilizer states, the
so called \emph{topological color codes} defined on a two-dimensional lattice
or \emph{2-colex}, are calculated. The topological entropy is used to measure
the entanglement of different bipartitions of the 2-colex. The dependency of
the ground state degeneracy on the genus of the surface shows that the color
code can support a topological order, and the contribution of the color in its
structure makes it interesting to compare with the Kitaev's toric code. While a
qubit is maximally entangled with rest of the system, two qubits are no longer
entangled showing that the color code is genuinely multipartite entangled. For
a convex region, it is found that entanglement entropy depends only on the
degrees of freedom living on the boundary of two subsystems. The boundary
scaling of entropy is supplemented with a topological subleading term which for
a color code defined on a compact surface is twice than the toric code. From
the entanglement entropy we construct a set of bipartitions in which the
diverging term arising from the boundary term is washed out, and the remaining
non-vanishing term will have a topological nature. Besides the color code on
the compact surface, we also analyze the entanglement properties of a version
of color code with border, i.e \emph{triangular color code}.

Quantum Physics;Strongly Correlated Electrons;High Energy Physics - Theory