  We report the $^{63}$Cu and $^{65}$Cu nuclear spin-lattice relaxation rate
measurements of cuprous oxide Cu$_2$O in a zero field Cu nuclear quadrupole
resonance at $T$ = 77$-$325 K. From the detailed isotopic measurements of the
relaxation rates, we successfully estimated a finite magnetic relaxation rate
$^{63}W_M$ and a predominant nuclear quadrupole relaxation rate $^{63}W_Q$.
$^{63}W_Q$ changed as $T^{2.1}$, while $^{63}W_M$ changed as $T^{1.6}$ or
$T^{\beta}\mathrm{exp}(-\it\Delta/T)$ with $\beta$ = 0.6(3) and $\it\Delta$ =
190(62) K. The nuclear spin scattering process due to a non-degenerate Fermi
gas was discussed as a possible candidate of the magnetic relaxation.
