  The entanglement and R\'{e}nyi entropies for spherical entangling surfaces in
CFTs with gravity duals can be explicitly calculated by mapping these entropies
first to the thermal entropy on hyperbolic space and then, using the AdS/CFT
correspondence, to the Wald entropy of topological black holes. Here we extend
this idea by taking into account corrections to the Wald entropy. Using the
method based on horizon symmetries and the asymptotic Cardy formula, we
calculate corrections to the Wald entropy and find that these corrections are
proportional to the logarithm of horizon area. With the corrected black hole
entropy expression, we then find corrections to the R\'{e}nyi entropies. We
calculate these corrections for both Einstein as well as Gauss-Bonnet gravity
duals. Corrections with logarithmic dependence on the area of the entangling
surface naturally occur at the order $G_{D}^0$ and it seems to be a general
feature of entanglement and R\'{e}nyi entropies for CFTs with gravity duals. In
particular, there is a logarithmic correction to the entropy in odd boundary
spacetime dimensions as well.
