the volume of the cube shaped box is 27^5 = 14,348,907 mm^3
the volume of this cube is s^3 = 14,348,907 mm^3 where s is the length of one side of the cube.
so we have 27^5 = s^3 --->>> log27^5 = log s^3 ---->>> 5 log 27 = 3 log s and since log 27 = 1.43136
we have 5 * 1.43136 = 3 log s -->>> 7.1568 = 3 log s =>>> log s = 7.1568/3 log s = 2.38560
and s= 243 mm check 243 x 243 x 243 = 14,348,907 mm^3