Although the normal vectors of the faces looks correct, the way the object is illuminated by the light source is wrong:
As you can see the light source is very close to the left side of the cube, yet it's not fully visible, but the front face is fully visible, and if I look the right side of the cube, I see this:
Which is also...weird.
What am I doing wrong? What and where should I check? If it matters, I generate an .obj file which I import later into Blender.
Here is the .blend file I'm using:


