Image taking $1$ of every $11$ possible nets of a cube, and then laying them out on a table. Now try to tape together their sides into a shape with no internal gaps, into a sort of net blob. If there must be internal gaps, then they must be able to be filled by other nets of a cube. Already hard enough, and I'm not sure whether or not it can be done, as I have searched online for quite a while and found nothing on the subject that answers that question. This is the first part of the question, and I am okay with the individual units of nets being different sizes from each other, i.e. one net folding into a cube with sides of $1$ and another folding into a cube with sides of $2$, but if it is possible for them to all use the same units then please do so.
The second part is even harder, and I have no clue where to even start solving it. Imagine trying this again, but the final shape you create has to also tile infinitely. I am also okay with this one using different units, even with separate net blobs using different units.
This may be too complicated a question or even outright impossible to accomplish, in which case please show me why, as I don't have much intuition on this problem. It is likely that the second half is impossible, but I can't really explain why it feels that way.
Here is one solution:
Image source: https://lsusmath.rickmabry.org/rmabry/dodec/cube/allCubesFlapping.html
I found this by googling "tile with nets of cube".