
If your 3D printer does indeed support color information you will have to look into its documentation what file formats it supports and what it uses for color information. Those are generally either procedural textures or voxel based textures for volumetric data representation (like smoke or sparse mediums) There is no such thing as '3D textures', at least not in the way you mention. UV coordinates are what is needed for 'wrapping' a 2D texture around a 3D mode, they can be either automatic, or obtained by UV Unwrapping It doesn't include any color or texture representation structures, as far as I know it doesn't even support UV Coordinates. The STL file format doesn't support textures, its a geometry only file format suited for 3D printing and computer based fabrication processes.

fbx export why there are no materials or textures? or Issue with Importing 3D Models into Blender Similar issues have been asked many many times before, see.
