How do i UV texture model with color and not image textures

Hello all
what i mean ( i dont know the blender / 3d term ) is that i want to texture for example cube that each face will have different color and then export it to FBX as model with UV mapping all of then within blender .
Thanks

Give each face a different coloured material. You can than bake the colour to a texture with the Render / Bake settings
or
Just in the Image Editor or external application (UVs / Export UV Layout menu) just paint the UV map with each face having a different colour

Supply an example file for review