That depends on the size of the little boxes.
If they're all 1-cubic-foot boxes, then you can fit (7 x 7 x 8) = 392 of them in there.
And by the way ... 7 x 7 x 8 is not a "cube".
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Assuming the boxes are each 1 foot in length, width, and height, you could fit 7x7x8 = 392 boxes in the 7 feet x 7 feet x 8 feet cube.
It can be challenging to put an eraser cube back together once it has been taken apart, as they are typically not designed to be reassembled. It may be best to consider getting a new eraser cube.
To find out how many 7 mm cubes fit in a volume of 3395799 cubic mm, you need to divide the total volume by the volume of one 7 mm cube (7 mm x 7 mm x 7 mm). The volume of a 7 mm cube is 343 cubic mm. Dividing 3395799 by 343 gives approximately 9905 cubes fitting in the volume.
There are lots of advantages to using plastic shoe boxes. The most common advantage is that you don't have to scramble around, going from box to box, trying to find what shoe you are looking for with ease. These boxes can also be stacked on top of each other without the crushing of paper boxes. They come in different shapes in order to fit every size of shoe whether it be a boot or a dress shoe. They are just totally more convenient for the shoe lover in you.
The maximum number of different phenotypes available in a dihybrid cross with 16 boxes in a Punnett square is 4. This is because there are four possible combinations of alleles for two traits that can segregate independently.
To compare that, if you can't find the planets' volume directly, take the diameter of each planet and cube it. Then divide.