Stretched surfaces

The edges of a cube are stretched, can you find the new surface area?
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Problem



The height, width and length of a cube are multiplied by 2, 3 and 6 respectively to create a cuboid.

The surface area of the cuboid is $N$ times the surface area of the original cube.

What is the value of $N$?

This problem is taken from the UKMT Mathematical Challenges.