A cube is 6 sided, counting front and back it's 12.
12 (12) = 144
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do you mean 12"x12"? if so 400+3%waste for cuts = 412..so 10 boxes.
180 square feet will fit a room 12 x 15.
-- Each tile covers 12" x 12" = 1 square foot.-- To cover 180 square feet, you need nominally 180 tiles.-- The number of boxes is 180/(number of tiles per box)-- If tiles are not sold in boxes of 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45,60, 90, or 180 to the box, then that quotient doesn't come out even. If they won'tsell you a part of a full box, then you'll need to round it to the next larger integer.
4509 divided by 12 = 375.75 or 375 boxes one box only three quarters full. So you would use 376 boxes.
There are infinitely many boxes that will fit 200 inch cubes and have space left over and the question does not exclude such boxes. However, there are 12 boxes that will just fit 200 inch cubes.