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The volume of a cube is calculated using the formula V = s^3, where s is the side length of the cube.
Given that the side length of the cube is 18 inches, we can calculate the volume of one cube:
V = 18^3
V = 5832 in.^3
Since there are 75 boxes to transport, we need to multiply the volume of one box by the number of boxes:
Total volume = 5832 in.^3 * 75 = 437,400 in.^3
Therefore, the service will need 437,400 in.^3 of space to transport the 75 boxes.