If the side length is increased by a factor of 3, how much larger is the perimeter of a face of the new cube?

The perimeter of a face of the new cube is 8 times larger than the previous cube.

Let us say, the side of cube before increase is "a"

Then perimeter of the cube = 12a,

because the cube has 12 sides.

And perimeter of a face of cube = 4a

Now, the side length is increased by factor of 3 i. e. new side is 3a

Thus, perimeter of new face of the cube = 4*3a = 12a

Therefore, the new perimeter is larger by = 12a - 4a = 8a