How to interpolate vertex colors in a cube? I have this model made out of cubes:

And I want to set the white cube some vertex colors, which correspond to the vertex's surrounding cube/cubes and interpolate between them. Note that this cube must be geometrically perfect, thus I don't want to be using any brushes or tools where I must draw freehand.
Is there any simple way of doing something like this?
In general - each vertex is usually used to store only one color. In your example one vertex consists from three colors. So the only one way to interpolate is to set average color.