1. **Problem Statement:** We are given a density function $$\rho(x,y,z) = \frac{2xe^{xy}}{(z^3+2)z}$$ defined inside a cubic block with dimensions 2m by 2m by 2m, where $$x,y,z \in [0,2]$$. We want to understand the density distribution inside the block. 2. **Understanding the function:** The density depends on all three coordinates. The numerator $$2xe^{xy}$$ grows with $$x$$ and $$y$$, while the denominator $$ (z^3+2)z $$ depends on $$z$$ and affects the density inversely. 3. **Key observations:** - For $$x=0$$, density is zero regardless of $$y,z$$. - For $$z=0$$, the function is undefined (division by zero), so the density is not defined at $$z=0$$. - As $$z$$ increases, denominator increases, reducing density. 4. **Summary:** The density increases with $$x$$ and $$y$$ but decreases with $$z$$ due to the denominator. Since the user did not request integration or further calculations, this explanation covers the density function behavior inside the block.