Answer
True.
Work Step by Step
The function $f$ is an odd function if $f(-x)=-f(x)$.
The function $f(x)=x^3$ is an odd function since:
$f(-x)=-x^3=-f(x)$
The function $f(x)=x^3$ is increasing on $(-\infty,\infty)$ as can be seen from the graph below.
