An empty cubical carton of side 7cm has the volume:
7 x 7 x 7 = 343cm³
A cube of side 1cm has the volume:
1 x 1 x 1 = 1cm³
From this, we can see that a 1000 cubes of side 1cm has the volume:
1000 x 1cm³ = 1000cm³
But we know that the cubical carton of side 7cm only has a volume of 343cm³.
Since 1000cm³ > 343cm³,
you cant fill 1000 cubes of side 1cm in such a carton.
TL;DR
No
Hope this helps
