How many times will the volume of a cube increase if all its edges are increased seven times?

The volume of the cube (V) is calculated by the formula:

V = a * a * a, where a is the length of the edge of the cube.

Let a1 be the edge of the cube, then a2 = 7a1 is the edge of the cube, increased by 7 times.

V1 = a1 * a1 * a1 = a13, V2 = a2 * a2 * a2 = a23 = (7a1) 3 = 343a13.

Find out how many times the volume of the cube will increase:

V2: V1 = 343a13: a13 = 343.

This means that the volume of the cube will increase 343 times.