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We present modified versions of existing criteria for the density propertyand the volume density property of complex manifolds. We apply this methods toshow the (volume) density property for a family of manifolds given by$x^2y=a(\bar z) + xb(\bar z)$ with $\bar z=(z_0,\ldots,z_n)\in\mathbb{C}^{n+1}$ and volume form $\mathrm{d} x/x^2\wedge\mathrm{d} z_0\wedge\ldots\wedge\mathrm{d} z_n$. The key step is showing thatin certain cases transitivity of the action of (volume preserving) holomorphicautomorphisms implies the (volume) density property, and then giving sufficientconditions for the transitivity of this action. In particular, we show that theKoras-Russell Cubic Threefold $\lbrace x^2y + x + z_0^2 + z_1^3=0\rbrace$ hasthe density property and the volume density property.

(Volume) Density Property of a family of complex manifolds including the Koras-Russell Cubic