  Using the corrected expression of Hawking temperature derived from the
tunneling formalism beyond semiclassical approximation developed by
\emph{Banerjee} and \emph{Majhi}\cite{beyond}, we calculate the corrected
entropy of a high dimensional Schwarzschild black hole and a 5-dimensional
Gauss-Bonnet (GB) black hole. It is shown that the corrected entropy for this
two kinds of black hole are in agreement with the corrected entropy formula
(\ref{entropy of apparent horiozn}) that derived from tunneling method for a
$(n+1)$-dimensional Friedmann-Robertson-Walker (FRW) universe\cite{FRW}. This
feature strongly suggests deep universality of the corrected entropy formula
(\ref{entropy of apparent horiozn}), which may not depend on the dimensions of
spacetime and gravity theories. In addition, the leading order correction of
corrected entropy formula always appears as the logarithmic of the
semiclassical entropy, rather than the logarithmic of the area of black hole
horizon, this might imply that the logarithmic of the semiclassical entropy is
more appropriate for quantum correction than the logarithmic of the area.
