The average value of a function f(x, y, z) over a solid region E is defined to be 1 favg f(x, y, z) dV %3D V(E) where V(E) is the volume of E. For instance, if p is a density function, then pava is the average density of E. Find the average value of the function f(x, y, z) = 3xyz over the cube with side length L that lies in the first octant with one vertex at the origin and edges parallel to the coordinate axes.

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