The cube of a negative number is positive.

The statement is False.

A cube of a negative number is always negative. For example,

Cube of (-5):

$-5\times -5\times -5=(-5\times -5)\times -5$

$-5\times -5\times -5=\left(25\right)\times -5$

$-5\times -5\times -5=-125$