Can you screencapture your Cube Animation for refference. Easier for us to Visualize what you describe with words (still confused after reading twice)
I was recently working on an unfolding animated cube in blender but when I tried to import it to UE4 I ran into problems getting the animation to work. After much trial and error the only way I found which worked was to build a skeleton and weight the sides of the cube 100% to their corresponding bones. Parenting a side to its corresponding bone any other way aside from weight painting resulted in an unuseable animation in UE4. Does UE4 only support weight painted skeletons? or am I unaware of a workflow pipeline that already exists.