I know how to pack $5$ unit squares in a square of side length $2+\frac{\sqrt{2}}{2}$. Is there an $\varepsilon>0$ such that there exists a packing of $9$ unit cubes in a cube of side length $3\varepsilon$?
(Inspired by this question.)
I know how to pack $5$ unit squares in a square of side length $2+\frac{\sqrt{2}}{2}$. Is there an $\varepsilon>0$ such that there exists a packing of $9$ unit cubes in a cube of side length $3\varepsilon$? (Inspired by this question.) 


Yes, since one can pack 10 unit cubes in a cube of side length $\:\:2+\left(\hspace{0.023 in}\frac12\hspace{0.05 in}\cdot\hspace{0.03 in}\sqrt2\right) \;\;$. See $\:$ stetson.edu/~efriedma/cubincub . 

