A venerated pass time of pedants is to point out that pictures of "Rubik's Cubes" (on t-shirts, posters etc.) are not actually solvable.
The first thing that should be checked is that the cube is made up of the right pieces. To be solvable a cube needs six colors each with nine squares. The cube also needs each edge and corner unit (these are the smaller cubes that make up the cube) to be unique. Not only must they be unique but if two center pieces are opposite each other no edge or corner piece can contain both of those colors.
Once you have a cube that is made up of all the right pieces you still need to verify it can be solvable. There are a couple of rules here, so I'll defer to an expert to explain them, the spoiler below explains how we can do this. If you are interested in solving the problem on your own you don't need to visit the site to understand or participate in this challenge.
Your task is to take a pattern as input and determine if it is in fact a solvable Rubik's cube. To be solvable there must be a way to perform valid moves on a cube so that the cube has only one color on each face (and the different faces have different colors). Most Rubik's cubes have a standard coloring (White is opposite Yellow, etc.) you may not assume that the solve state follows this particular coloring.
A valid move is either the clockwise or anti-clockwise rotation of a single face of the cube. With the rotation of the face of the cube any squares bordering the face are rotated as well, staying connected to the face they were previously touching.
You may take the cube in any reasonable manner. If your language has some builtin "cube-face" type, good for you, that is fine as input, other wise you can take a 2D array of the net, of the cube, 1 3 by 3 lists for each face. Just be reasonable. If you want to know if a specific format is acceptable comment or ping me in chat and I will add to the challenge to state its validity.
Your input format need only support up to 9 possible colors.
For output this is a decision problem so you should output one constant value for "Yes, this is a valid Rubik's cube" and one different constant value for "No, this is not a valid Rubiks cube".
This is code-golf so answers will be scored in bytes with less bytes being better.
Here are test cases. They are formatted as the net of a cube with each square as a single letter. Different letters represent different colors. Any more testcases can be added upon request.
RRR RRR RRR GGGWWWBBBOOO GGGWWWBBBOOO GGGWWWBBBOOO YYY YYY YYY GRR GRR ORW WWRBWYBOOGGY GGRBWGYBBOOO OOGRWGYWWRBB WYO YYB YYB
RRR RRR RRR GGGWWWBBBOOO GGGWWWBBBOOO GGGWYWBBBOOO YWY YYY YYY RRR RRR RRR GGGWWWBBBOOO GGGWWWBBBOOO GGGWWWBBBOOO YWY YYY YYY RRR RRR GGG GGYWYWRBBOBO GGYWWWROBOOO GGYWWWRBBOOO BBB YWY YYY RRW RRW GGG GGYWWYEOBROO GGYWWYEBBROO GGOWWYWBBROO BBB YYW YYO