7. If a small ball with a radius of 1 can move freely in all directions inside a regular tetrahedron container with an edge length of $6 \sqrt{6}$, then the area of the container's inner wall that the ball can never touch is $\qquad$ .
7. $120 \sqrt{3}$.

Considering the circumscribed regular tetrahedron of a small sphere with radius 1, it is easy to know that its edge length is $2 \sqrt{6}$. Therefore, the area of the container's inner wall that the small sphere can never touch is
$$
S=\sqrt{3}\left((6 \sqrt{6})^{2}-(4 \sqrt{6})^{2}\right)=120 \sqrt{3} .
$$