The volume of a cubical box is given by the formula:
V = l^3
where l is the length of one edge of the cube.
In this case, the length of the box is given as 12 cm. Since it is a cube, all three dimensions are equal, so the length, width, and height are all 12 cm.
Thus, the volume of the box is:
V = 12^3
= 1728 cubic centimeters
Therefore, the volume of the box is 1728 cubic centimeters.