Suppose there was some small ball inside of your super-packed structure that isn’t filled. Then we can fill this ball, and so the structure isn’t super-packed. It follows that the volume of the empty space inside of your structure has to be 0.
Now, what does your super-packed structure look like, given that it’s a empty cube that’s been filled?
EDIT: Nevermind, just saw that Villiam gave a similar answer.
Maybe think about the problem this way:
Suppose there was some small ball inside of your super-packed structure that isn’t filled. Then we can fill this ball, and so the structure isn’t super-packed. It follows that the volume of the empty space inside of your structure has to be 0.
Now, what does your super-packed structure look like, given that it’s a empty cube that’s been filled?
EDIT: Nevermind, just saw that Villiam gave a similar answer.