In C4D, make a null, make it the parent of a cube and rotate the null. Or make a cube, rotate it, and make a the parent of a null. Apply and External Compositing tag to the null. Render in C4D and select “include 3D data”.
In AE, make the null a parent to the video layers you want to see on the cube. Position them at the same position as the null (use an expression if necessary), then move them so they line up with the sides of the cube. If, for example, your cube is 200x200x200, you should have to move each side 100 pixels away from the null in either the X,Y or Z direction.
Or you may want to apply the video to the cube in Cinema 4D before going into AE.