What units can measure density?

$\text{Density}$ $=$ $\text{Mass"/"Volume}$
So we can have the quotient of any mass units and any units of volume. Given that ${m}^{3}$ are an impossibly large volume, chemists typically use $g \cdot m {L}^{-} 1$ or $g \cdot {L}^{-} 1$.