The formula for calculating the surface area of a cuboid is: S = 2(ab + bc + ca), where a, b, and c represent the length, width, and height of the cuboid respectively.

This formula represents the sum of the areas of the six faces of the cuboid. Since opposite faces of a cuboid have equal areas, we can first calculate the areas of the top and bottom faces, then the areas of the front and back faces, and finally the areas of the left and right faces.

By adding the areas of these three parts together and multiplying by 2, we can obtain the total surface area of the cuboid.

The principle underlying the cuboid surface area formula is to decompose the cuboid into six rectangular faces, calculate the area of each face, and then sum up the areas of all six faces to arrive at the total surface area. The derivation of this formula is achieved through geometric analysis and calculation.