Turning Cuboids Into A Cube

$\text{Side of the cube formed by N cuboid As} = \text{LCM of }1,3,2 = 6 \text{ units}$

$\text{Surface Area of the cube} = 6×(6)^2 =$ $\large \boxed {\color{#20A900}{216 \text{ unit}^2}}$

The cuboid has a volume of $1 \times 2\times 3 = 6$ units. Therefore the cube's volume must be a multiple of 6. The smallest cube that satisfies this condition has dimensions $6\times 6\times 6$ .

It is easy to check that this cube can actually be built from the given cuboid: place 2 lengthwise, 3 next to each other, and 6 on top of each other.

The area of the cube is $6\times 6^2 = \boxed{216}$ .