How can I determine if a certain Rubik's cube, that is in a certain state, is solveable? By "certain state" it could mean that the cube has been dismantled and put together again. And in my experience if you don't put it together the right way, the cube might not be solvable.

A way to check for a 3x3x3 cube would be great. For any size cube, awesome!

How can I determine if a certain Rubik's cube, that is in a certain state, is solveable? By "certain state" it could mean that the cube has been dismantled and put together again. And in my experience if you don't put it together the right way, the cube might not be solvable.

A way to check for a $3 \times 3 \times 3$ cube would be great. For any size cube, awesome!