Answer
$$1$$
Work Step by Step
Our aim is to integrate the triple integral as follows:
$$ Average=\dfrac{1}{8}\int^2_0 \int^2_0 \int^2_0 xyz \space dz \space dy \space dx \\=\dfrac{1}{4}\int^2_0 \int^2_0 xy \space dy \space dx \\=\dfrac{1}{2} \times \int^2_0 x \space dx \\=1$$