Solution
= Solution
A volume mean is the <volume integral> of the <temperature> divided by the <volume>. On this cube,
$$
\overline T=\frac1{2^3}\int_0^2\int_0^2\int_0^2xyz\,dx\,dy\,dz
=\frac1{8}\left(\int_0^2x\,dx\right)^3.
$$
Each one-dimensional integral is two, giving
$$
\boxed{\overline T=1.}
$$
The number is in the temperature units implicit in the given field law and coordinate units.