363 x 81 is a perfect cube.

False

$\because \quad 363 \times 81=3 \times 11 \times 11 \times 3 \times 3 \times 3 \times 3$

$=3 \times 3 \times 3 \times 3 \times 3 \times 11 \times 11$

Grouping the factors in triplets of equal factors, we have

$363 \times 81=(3 \times 3 \times 3) \times 3 \times 3 \times 11 \times 11$

Clearly, in grouping, the factors in triplets of equal factors, we are left with two factors $3 \times 3$ and $11 \times 11$.

Hence, $363 \times 81$ is not a perfect cube.