Given that, $f(-x) = \left\{\begin{matrix} f(x) ; & even \\ -f(-x) ; & odd \end{matrix}\right.$
$f(x) = |x|^{3} \longrightarrow (1)$
We know that $f(x) = |x| = x $
$\qquad f(-x) = |-x| = x $
So, $f(x) = |x| $ is even function.
Now, $f(x) = |x|^{3}$
$\Rightarrow \boxed{f(x) = x^{3} (odd)}$
Correct Answer $: \text{B}$