Camera exposure changes although settings stay the same except focal distance. Why?

I have a Nikon D90 and recently got a Sigma 18-50 f/2.8-4.5 (first wide lens i ever had). Being used to my 50mm prime, i never noticed this before:
If, for example, i set the exposure to 1/125th of a second and f/6.3 i can take a certain picture outside, correctly exposed at 18mm. If i zoom in to 50mm, it underexposes although the lens can do that f-stop at 50mm.
I noticed this while trying to film something and wanted to zoom in while shooting. Any ideas?

PS: I only use manual exposure, so nothing else but the focal distance changes.

As focal length increases, less light is able to travel down the length of the lens, resulting in underexposure. Think of it this way, if you look through a paper towel tube, a fair amount of light travels down the tube and to your eye. However, if you look down a 6 foot pipe with the same diameter, much less light travels down the length of the tube to your eye.