Edge length of the side of a cube = 5 inches
Then
Volume of the cube = (side)^3
= (5)^3
= 125 inches ^3
So the volume of the actual cube is 125 inches^3
Now after the side lengths are triple, then
New edge length of each side = 3 * 5 inches
= 15 inches
Then
New volume of the cube = (New side)^3
= (15)^3
= 3375 inches^3
Then the volume of the new cube is 3375 inches^3
So
The number of times the volume of the new cube is greater = 3375/125
= 27
So the volume of the new cube is 27 times greater than the old cube.