Seeing the inside of a cube when motion blur is enabled

You have a couple of options. First, because the Alpha Edges of the cube are antialiased, you are going to get some transparent pixels. Second, 3D layers in After Effects have no Z depth. They are not one pixel thick, they are zero pixels thick so you can't make a perfect seamless edge, but you can help it by setting the blend mode of every layer to Alpha Add. 

That trick may help with slow-moving layers, but if you want to block the see-through you have to create some chamfered corners with black layers at a 45* angle inside your cube. A little math and offsetting the anchor point can help you assemble this inside structure for your 3D layer cube to hide the edges. 

Another option is to pre-compose the cube and then add Pixel Motion Blur to the nested comp. You'll also have to copy any lights in the scene to the nested comp and make a duplicate camera in the Pre-comp that is tied by expressions to any camera movement in the Main comp because Collapsing Transformations will let the edges show through. 

A much simpler solution would be to make your Cube with shape layers, export the cube to C4D, and then use C4D lite to include the cube in the main comp. 

An even better solution is to invest in a 3rd party app like Element 3D from Video Copilot. That's my preferred solution.

Show us a screenshot of your comp and timeline and we may be able to provide an answer.

Mylenium