Consider a beam with a square box cross-section as shown in the figure. The outer square has a length of $10 \: \mathrm{mm}$. The thickness of the section is $1 \: \mathrm{mm}$.
The area moment of inertia about the $x$-axis is $\_\_\_\_\_\_ \: \mathrm{mm}^{4}$ (in integer).
