7. A small sphere with a radius of 1 can move freely in all directions inside a regular tetrahedron container with an edge length of $4 \sqrt{6}$. The area of the container's inner walls that the sphere can never touch is $\qquad$ .
7. $72 \sqrt{3}$

Analysis: Consider the circumscribed regular tetrahedron of a small sphere with radius 1, it is easy to know that its edge length is $2 \sqrt{6}$. Then the area $S$ of the container's inner wall that the small sphere can never touch is $S=\sqrt{3} \cdot\left((4 \sqrt{6})^{2}-(2 \sqrt{6})^{2}\right)=72 \sqrt{3}$