6x6x6 cube with smooth plates on bottom? Adult, returning to Legoland and the world of LEGO.

I'm interested in building a static 6x6x6 cube that is smooth on all six sides. I can see how to get the top smooth, using an appropriate build up with blocks and plates, and capped with smooth tiles. 

The sides are easy, of course, just being the sides of blocks and other pieces.

But what about the bottom? What works for reversing the studs, so that smooth tiles can be used for the final finish on the bottom?

I would like the final build to be rock solid, exactly 6x6x6 -- no movement like a rubik's cube needed at all.

Just interested in best techniques for a smooth bottom, before I order parts for my bigger build. Want to limit pieces to standard blocks, plates, and smooth tiles.

Suggestions, threads to review, links to solutions?

PS: Sorry I couldn't post tags like: "6x6x6 cube tiles smooth"; suggestions welcome.
While there could be various approaches building studless the easiest one would be with Tile, Modified 2 x 2 Inverted. These modified tiles have studs on one side, which fit under bricks and plates, and smooth surface on the other side.



Here is a prototype which features equal 6-stud (or 30 modules) long sides. Parts can be changed upon availability, but it gives the idea how high you need to go to reach 6-stud height. Red parts are modified tiles mentioned above.