This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better.
Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.
To any future monthly posters of SQ threads, please remember to add the "stupid_questions" tag.
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.