Question

Why do you use cubic units and not square units to find the volume of a solid figures

Answer 1

Because you can't build a solid figure with little squares.
You need little cubes.

Answer 2

Since volume is the amount of space inside a object that is 3D you need to use cubic units also represented by the cubed exponent. This is because in square units your seeing how much space is in a square, or circle, or something that's 2D, you get it? Whatever the dimension is that's what the exponent of the unit will be, so like a volume of a cube is 125 m^3 because it's 3d.