I wanted to know if there is a way of telling blender that volume objects should only show the volume, the fog and stuff when it is overlapping with a light source. I was trying to replicate the Youtube tutorials on how to make Volumetric light, but it does not really do the trick for me. I don't want to have the fog EVERYWHERE inside the cube, but only when where for an example a light cone is shining.
Answer: Okay, thanks to the comments I was capable to find the problem, it was the emission property of the principled volume in the shading editor for the volume material that is set on the volume cube. I just set it to 0, and it gives me the desired effect now.