Light passing through mesh

I took the default cube and added a sun lamp instead of the default point lamp. I pointed the sun facing a side. After doing that I deleted one of the sides the sun was not facing and I rendered it. When I looked into the cube I saw that the sun was lighting the inside face as well. I did this on blender game engine using GLSL. Is there a reason that happens and how can I fix it.

I turned shadows on and it semi fixed my problem but I has these weird lighting glitches.