  We provide a detailed analysis of 12 XMM observations of the nearest
persistent extragalactic ultraluminous X-ray source (ULX), M33 X-8. No
significant spectral evolution is detected between the observations, therefore
we combine the individual observations to increase the signal-to-noise ratio
for spectral fitting. The combined spectra are best fitted by the
self-consistent p-free disk plus power-law component model with p =
0.571_{-0.030}^{+0.032}, kT_{in} = 1.38_{-0.08}^{+0.09} keV, and the flux ratio
of the p-free disk component to the power-law component being 0.63:0.37 in the
0.3 -- 10 keV band. The fitting indicates that the black hole in M33 X-8 is of
\sim 10 M_{\odot} and accretes at a super-Eddington rate (\sim 1.5 L_{Edd}),
and the phase of the accretion disk is close to a slim disk (p = 0.5). We
report, for the first time, that an extra power-law component is required in
addition to the p-free disk model for ULXs. In super-Eddington cases, the
power-law component may possibly result from the optically thin inner region f
the disk or a comptonized corona similar to that of a standard thin disk.
