When you UV Map a cube (a single object) then by default, the entire object is UV Mapped.
When you apply a colour or texture maps to that cube, it will be applied to all of the cube, and any texture map, will be positioned according to the UV Mapping direction you specified.
If you want to have “Different” shaders, applied to each of the sides of the cube, you would either create a set of “Shading domains” (one for each side of the cube) .. or, you could use a single shader and a texture map with different textures in the areas where each side is depending on the UV Mapping type and layout options you’ve selected.
In the UV Mapping options for “box mapping”, there are three layout options, ..Each of these “Layouts” will change the position of the flattened Cube “Wire-frame, in the UV Mapping grid.
You can Export that flattened Wire-frame “layout” as an image, which can then be used as a “template” to position photo’s or textures, to create a final “Texture Map”, which can be applied to your Cube model. (see pic 1)
In Carrara’s shader room, you can also create a “layers list” shader, where each shader in the list can have different colours, values, or texture maps, and can be applied to the Cube using flat mapping which allows you to specify the placement of each shader
EG: top, left, right, front, back, bottom. (see pic 2)
Pic 3 shows Layers list,.. Multiple shaders on multiple domains, and a single texture map on a single shading domain.