Given a system with N identical Fermions, with spin $\frac{1}{2}$ and mass $m$, subject to the potential:
$V(\vec{r}) = \frac{1}{2}m\omega^{2}(x^{2}+y^{2}+z^{2})$  

and the single particle energy levels:  

$E\_{\vec{n}} = \hbar\omega(n\_{x}+n\_{y}+n\_{z}+\frac{3}{2})$,

Calculate the Density of states $g(\epsilon)$.

I know that the density of states is the number of single particle states with energy between $(\epsilon,\epsilon +d\epsilon)$, per unit energy.

If we define $F(\epsilon)$ = #States with energy $<\epsilon$,  

then $ g(\epsilon) = \frac{dF(\epsilon)}{d\epsilon}$

I am unsure how to get this #States in either case.