Ok, so 6 faces of LEDs, not a whole cube. No matter.
I only provided the means to display the data that represents the state of the LEDs.
You will have to develop the algorithm for deciding when that data changes, from 1 face being on, shifting to 4 faces being partially on in various amounts as the cube is tipped and/or rotated in various manners.
So Imagine you will also need some kind of 3-D angle sensor also to get that information from.