The sides of the Lego dice are interchangeable, allowing dice that can be modified on the fly (even during the middle of a game if necessary). There's heaps of potential there, but what about other cubic forms that have an inherently changeable structure.
Most people with a vague familiarity with western popular culture or toys from the last 25 years will have a knowledge of the coloured cube with the rotating sides.
But how could it apply as a mechanism in a roleplaying game?
The same might have been said about a Jenga tower before someone conceived of using it's inherent tension as a metaphor for fear within the narrative.
The symbolism of a Rubik's cube could be transferred between the narrative of the in game evenets and the mechanisms of the real world quite easily.
The first idea to come to mind is a structured universe reflected by a completely solved cube, while a chaotic universe would be reflected by a jumbled cube.
A game about scientists trying to overcome a chaotic universe might involve turns where each player makes twists of the cube based on their skill potential (basic skills might allow a player to make a single twist, intermediate skills might allow two twists, advanced skills three twists). Players get a number of successes on their action by looking at the sides of the cube with matching colours. 2 matching colours on a side equals 2 degrees of success, 6 matching colours equals six degrees of success, a full matching side equals nine degrees of success.
Fulfilling a complete side might be symbolic of achieving a certain effect within the story, different side colours might reflect different storylines. Players could then show which storylines they are trying to resolve by trying to solve a particular side of the cube, other players could work with the agenda of sabotaging certain storylines while trying to resolve others. Antagonists might even have the agenda of simply trying to prevent sides being solved.
A few other developments evolve from this mechanism. The first is that most good successes build on the successes of the past. A player can usually only complete a side once a few other players have made some substantial headway on achieving that goal.
The second is that other sides might go through degrees of improvement or degradation as a single side of the cube is focused upon. The characters find that their actions have ramifications beyond their intentions (for the positive or negative).