CareerCup

with reference to stackoverflow 500221. here is a DS

class Square
    + name : string
    + accronym : string

class Row
    + left_square : square
    + center_square : square
    + right_square : square

class Face
    + top_row : list of 3 square
    + center_row : list of 3 square
    + bottom_row : list of 3 square

    + rotate(counter_clockwise : boolean) : nothing

class Cube
    + back_face : face
    + left_face : face
    + top_face : face
    + right_face : face
    + front_face : face
    + bottom_face : face

    - rotate_face(cube_face : face, counter_clockwise : boolean) : nothing

What do you mean by backend database portion? Since a cube has 6 faces, each face has 9 squares, can we just represent it by an array that's 54 items in length?

a[i] can have color of the element i.

(Using 1 as starting index for simplicity) a[1-9] = face1, a[10-18] as face2 and so on.

For a 3x3x3, we have 27 smaller cubes

1 at the center, no color
6 at the center of each face, 1 color
8 corners, 3 colors
Remaining 12 with 2 colors

That sums up to 54.

Since they asked Rubiks cube I believe we can leave out the center 1/ 27 cube. Basically we divide a cube into
6 centers
8 corners
12 edges
But this is only the numbers of squares
visible now we have to account for filling the six colors.

So an array of (3x3) x6 should be sufficient to hold a cube configuration.