Chapter R - Review of Basic Concepts - R.2 Real Numbers and Their Properties - R.2 Exercises - Page 22: 113

$x$ and $y$ must have the same sign.

For the expression $\dfrac{x^3}{y}>0$ to be true, $x^3$ and $y$ must have the same sign. Note that $x$ and $x^3$ have the sign. As a result, if $x$ and $y$ have the same sign then the expression $\dfrac{x^3}{y}>0$ will be true.