1: Unwrap the cube using the Reset option. This will stack all the faces one on top of the other Each completely filling the UV space.
2: Edit each of the UV islands (faces) so that they are orientated correctly.
3: In the UV editor Properties side panel, enable the Normalized option. Doing this will mean if you select one of the islands and move it 1 unit in the X axis it will move exactly one UV space to the right. (Disabled it would move only 1 pixel).
4: Face +X is already correctly positioned (first in the line).
In the 3D editor select face -X.
5: In the UV editor move this -X face UV island 1 Unit to the right. G X 1 Enter
6: In the 3D editor select the next face in the line, +Y.
Back in the UV editor move this select island 2 units, G X 2 Enter.
Repeat for the remaining faces, G X 3 Enter. G X 4 Enter. G X 5 Enter.
7: UV Editor, UV's menu check Constrains to Image Bounds
8: Set the Scaling pivot point to 2D Cursor.
9: Using the UV Properties panel, Display menu, set the 2D cursor location to the 0.0 0.0 position in the UV space.
10: To get the line of UV islands exactly back into the UV space we need to scale them by 1/6. S 0.16666666 Enter.