This is a good opportunity to apply the principle of keeping it "down and dirty" (read cheap and easy).

First, source a commonly available CRS strip steel, in a width suitable for the tiles, that also comes in various thicknesses (give yourself room to adjust thickness). Offhand, I think thinner (18-20ga.) would be better. You can scale the cube to suit the strip width. Shear the strips to the required lengths. Clean up the burrs on a belt sander (in production, this can be done by tumbling). Powder coat the tiles the required colours. Glue the tiles into place.

All the above processes and materials are economical, and some processes you may even be able to do yourself.

For production, you may consider an injection molded foldable base with insets for the tiles (would allow the product to be shipped flat; see ProtoMold sample cube), and/or stamped/formed steel strips/panels which resemble a tiled surface.

Have fun!

Gerry

 

Cast iron is not really practical. 2mm is a little thin, the parts are small, and it can be done just as better with other materials.

why are the large faces cut into strips? why not just one bigger piece? Do the players move/ remove the tiles as part of the game? You could also probably come up with a clever way to make it so that the cube splits open so that the game pieces can be kept inside. Then you get rid of the need for a box, and the playing surface is there to entice you into playing a game.