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The formula for the volume of a cube is V = side length^3.
Given that each box has a side length of 18 inches, the volume of each box is 18^3 = 5832 cubic inches.
To find out how much space the service will need to transport all 75 boxes, you need to multiply the volume of one box by the total number of boxes:
5832 cubic inches * 75 boxes = 437,400 cubic inches
Therefore, the service will need 437,400 cubic inches of space to transport the 75 boxes.
Answer: 437,400 in.