Answer
Diverges
Work Step by Step
Consider $a_n=\dfrac{(-3)^n}{n^3 2^n}$
Now, $l=\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_{n}} |=\lim\limits_{n \to \infty}|\dfrac{\dfrac{3^{n+1}}{(n+1)^3 2^{n+1}}}{\dfrac{3^n}{n^3 2^n}}|$
Thus, we have $l=(\dfrac{3}{2}) \lim\limits_{n \to \infty}|(\dfrac{n}{(n+1)})^3|=(\dfrac{3}{2}) \lim\limits_{n \to \infty}|(\dfrac{1}{(1+1/n)})^3|$
So, $l=\dfrac{3}{2} \gt 1$
Hence, the series Diverges by the ratio test.