The original cube has $6 $ faces, so its surface area is $6$ original faces.
Using a diagram can help show how the cube grows:
The cuboid's faces are $2$ by $3$ original faces, $2$ by $6$ original faces and $3$ by $6$ original faces, as shown in the diagram, and each appears twice.
The surface area of the cuboid is $2(2 \times 6 +2 \times 3 +3 \times 6)=72$ original faces.
The surface area of the cuboid is $N$ times the surface area of the original cube.