The dimensions of a Kleenex box are length, width and height. The volume of the box is equivalent to length times width times height.
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The acceleration due to gravity is the same for all objects near the surface of the earth - whatever their mass. The only way you will get a difference is if the air resistance is sufficient to slow one of the objects to a measurable extent.
As long as the cubes are 1x1x1 then any box with an equivalent volume would hold the same number of cubes. The volume of the 3x4x10 box is 120. So a box with the dimensions 1x1x120 would work just as well as a box with the dimensions 12x10x1 or 2x5x12.
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It sounds like you have already found the dimensions of the box.