Because the cross section of a cuboid is square, the width of the cuboid is equal to the height.

The increased surface area of a cuboid can be regarded as a cuboid with a side protruding by 5cm, that is, the increased area is a rectangle with a side width of 5cm.

Solution: Let the width = height = x of a cuboid.

80=5x*4

x=4

So the original cuboid volume is: 4*4*40=640.