This ACM Paper describes several alternative ways that it has used to represent a rubik’s cube and compares them against eachother. Sadly, I don’t have an account to get the full text but the description states:
Seven alternative representations of Rubik’s Cube are presented and compared: a 3-by-3-by-3 array of 3-digit integers; a 6-by-3-by-3 array of literals; a 5-by-12 literal matrix; an ll-by-ll sparse literal matrix; a 54-element vector; a 4-dimension array; and a 3-by-3-by-3 nested array. APL functions are given for orientation moves and quarter-turns plus several useful tools for solving the cube.
Also, this RubiksCube.java file contains a pretty clean representation along with the relevant code for rotating the sections (if you are looking for actual code). It uses a cell and faces array.