If its height is reduced by 4 cm, it becomes a cube, that is to say, its bottom is a square with equal length and width, and its surface area is reduced by 96 square cm. If the area of four rectangular rows is reduced, the area of each rectangular row is 96÷4=24 square centimeters, and its height will be reduced by 4 centimeters.

Then it can be calculated that the width of the cuboid is 24÷4=6 cm. Now it has been concluded that the length and width of the original cuboid are all 6 cm, and the height is 6+4= 10 cm, so the volume is 6×6× 10=360 cubic cm.