Answer
$$W=0.$$
Work Step by Step
The Wronskian of $\left\{1, x, x^{2}, x^{3}\right\}$ is given by
$$W=\left|\begin{array}{cccc}{1} & {1} & {x^{2}} & {x^{3}} \\ {0} & {0} & {2} & {3 x^{2}} \\ {0} & {0} & {2} & {6 x} \\ {0} & {0} & {0} & {6}\end{array}\right|=0.$$