Answer
The end behavior of $f(x) = -2x^3$ on $(-\infty,+\infty)$ is given by $$\lim\limits_{x \to -\infty}-2x^3=+\infty$$ and $$\lim\limits_{x \to \infty}-2x^3=-\infty$$
Work Step by Step
As $x$ grows to $\infty$, $2x^3$ grows to positive infinity, hence $-2x^3$ grows to $-\infty$.Similarly, when $x$ grows to negative infinity, $-2x^3$ grows towards $+\infty$.