It sounds interesting, I have not done anything in 3D, but I have some experience with images.
For my chess program, I didn't want to have to load images in, I was getting lots of problems trying to load images inside a jar into the program, so what I did was scan the images to get the colours of each pixel (in ARGB), store this data in arrays inside classes. Then create BufferedImages using this new data. So when you run the jar on desktop, or the applet version of jar on internet, it just builds the images of the chess pieces after loading.
Anyway, I think that is best just for small images, but maybe of use to you. You will need to stretch/scew the images when you rotate the cube (don't know if java 3D package deals with this ?)
I'll take a look at the code anyway, let me know how you plan to deal with the images if you want.
I've just ran the program, its cool, but I think rubiks cubes are infuriating difficult unless you are very smart. Anyway I'm gonna put the code in my IDE, and see if I can get an image on one of the faces, I'll let you know how I get on.
Thanks
Colin