Ok, it's been like more than 3 months now since that cube is making everyone either very angry or very intrigued. So, since that cube will most probably be gone in the next version, here's the highly-searched explanation of it. Before I continue, I am sure that some (or more) people will feel that this just sucks, or some other people will feel that I was very cinical when I designed this so-called easter-egg.
So here it is: take
"HyperIM game" without the quotes. A standard ASCII string, 8 bits / character, ISO standardised etc. Now the only problem with this representation is that it's in base 2 (you can also say that it's in base 8 or even 16 - hex!). Whatever.
Now we have the Cube which has only 6 sides. Why not convert the base-2 string into base 6? And what do you get? It's something like:
2324410331533515023513440540125013202212 <- this is "HyperIM game" in base-6 !
Now this seems like a reasonable amount of digits. The only catch next is that this are just digits in base 6, not actual symbols. The symbols on the cube start from "one" and end with "six". So, the first few correct moves to go throughout the game would be
"three" "four" "three" "five" "five".
If I would have been even more mean, I could have just swapped the base-6 digits with random symbols instead of o natural order. For example, digit 0 could have been the three-dotted side, and digit 5 could have been the four-dotted side.
That's all. Now you can go to sleep in case you had white nights trying to break the cube's mistery

References (just to test that I'm not making this up):
Online script to convert a string to base 16Online script to convert numbers from base to base