Answer
Diverges
Work Step by Step
Let us consider $a_n=\dfrac{(-3)^n}{(n^3) (2^n)}$
Apply ratio test.
$\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_{n}} |=\lim\limits_{n \to \infty}|\dfrac{\dfrac{3^{n+1}}{(n+1)^3 2^{n+1}}}{(\dfrac{3^n}{n^3 2^n})}|$
$\implies \dfrac{3}{2} \cdot \lim\limits_{n \to \infty}|(\dfrac{n}{(n+1)})^3|=\dfrac{3}{2} \cdot \lim\limits_{n \to \infty}|(\dfrac{1}{(1+\dfrac{1}{n})})^3|=\dfrac{3}{2} \gt 1$
Hence, the series Diverges by the ratio test.