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Yes this is possible with OpenCV. You will have to look at

1. Making sure that you compensate for camera deformation.
2. Defining the area of the rubics cube itself, by trying to find its outer boundaries.
3. Then taking the corner points to transform the image to a standard squared area.
4. Now find the crossing points of the seperate elements, defining individual regions of interest.
5. Start doing color analysis on each position.

If you're just starting OpenCV, start by going through the basic tutorials first, then this might be a very nice project to start of with!