If $m$ is a natural number such that $3^{m}=81$, what is the value of $m^{3}$?
(a) $81^{3}$
(b) $3^{81}$
(c) 64
(d) 24
(e) 48
The correct option is (c).

We have $3^{m}=81=3^{4}$, hence $m=4$. Therefore, $m^{3}=4^{3}=4 \times 4 \times 4=64$.