Directional Lights influence the wrong normals [updated]

Hi,

I have a problem with the directional lights. I try to set up a "sun" so I use 6 directional lights, one for each direction. All my objects are cubes and the normales are set up correctly. If I use a Point Light and turn off different normals for different cube faces, it works properly and I see black for 0.
But if I use the 6 directional lights, which are all perpendicular to each other and perpendicular to the cubes, the light adds up and for example, a light which is oriented on the...

Directional Lights influence the wrong normals [updated]