First off I want to thank JooJaa for replying to my previous post Help Needed With Animating A Rubik, a simple way. This got me pointed back in the right direction and was extremely helpful.
However I have run into some more problems....
My new set of problems revolves around some abnormal motion when using Quaternion rotation as the default for animating the cubes 90 degree rotations. The problem occurs after I have rotated and keyed a set of blocks (side A key 1), rotated an adjacent side (side B key 2) and then keyed the original side (side A key 3) initially for another rotation so the blocks do not go out of sync. So the rotational values of the blocks of side A, that were not constant between sides A and B, have remained constant(In other words the values for the angular rotation have not change for the blocks that were not rotated with side B from key frame 1 to key frame 3). When this happens there is a good chance that one or all of these blocks will exert strange motion that is random and abnormal. Upon examination of the graph editor the subsequent curves, related to the effective blocks, look as if someone has taken a pen and scribbled over the graph. After reading through the documentation on rotational interpolation on both Euler and Quaternion I discovered that there are inherent difficulties in interpreting the graph of Quaternion rotation, however, I do not believe this phenomenon to be normal behavior.....
I did, however, discover a work around for this abnormality in the rotation. Whenever I encountered this, what I believe to be an error in the calculated rotation curve, I simply applied Euler interpolation to the whole graph for the whole cube (all 27 block) and then reapplied Quaternion interpolation forcing Maya to recalculate the curves. This method seems to work but I am growing concerned about the affects of this fix over the long-term....
On my first attempt using the method suggested by JooJaa, and my work around for the abnormality, I encountered a point where the angular measures for the rotation angles were no longer whole number values. I can't say with any certainty what caused this behavior because I had the rotation tool set to 15 degree whole number increments. It was my assumption that the rotation angles would always be whole numbers if I increment in 15 degree steps but after several increments the rotation channels showed some of the angles as other than whole number values. It seemed to me that the problem of angle creep intensified the more times I rotated any one of the sides of the cube. It seems to me that at the points where I keyed the animation the rotation channels should show angles that are integer values of 90 degrees exactly, but that's not what is happening. I'm concerned that the converting back and fourth between Euler interpolation and Quaternion interpolation, to fix the weird behavior problem for the animation, may be causing the angle creep. Is this problem always associated with converting back and forth between Euler interpolation and Quaternion interpolation? Or is this angle creep expected to happen even if you don't recalculate between Euler interpolation and Quaternion interpolation? Either way is there any way to fix this problem so that at the end of an animation that requires many rotations the rotation channels will show angles that are integer values of 90 degrees exactly?