"God is dead and the optimal packing of squares killed him." I will never not think of this meme when looking at these horrors. I see it, but I don't like it. ;)
Isn't this obvious? Why do you need a proof for it, just stack the cubes next to each other? If we're talking infinitesimally thin squares, then stack them on top of each other? Am I missing something?
Look at some of the other links people have posted for optimal packings. The optimal 11 square packing looks nothing like what you're describing ("just stack the cubes next to each other").
The triangular view is most interesting. And a 20 minute video on this view is at https://youtu.be/uL5wuiy34rs
https://startupfortune.com/ai-models-formally-proved-walter-...
https://vplevris.medium.com/eleven-squares-one-tiny-gap-and-... (written just days before the new proof!)
https://jlevy.github.io/squares/cases/11.html
For more packings (circles in circles, etc) check out this page: https://erich-friedman.github.io/packing/index.html
EDIT: I found it a few links down. https://jlevy.github.io/squares/cases/11.html
https://jlevy.github.io/squares/