Is extreme fatigue due to cancer, or just what happens during cancer treatment?

Both. Fatigue may be presenting symptom of many cancers. Treatment with chemotherapy and radiation add to the fatigue.
Both. Cancers are highly active cells and they consume the resources of the persons body very fast. Cancer treatments can also make a person tired due to damage to normal cells that occurs and the repair process. This is a very simple explanation of the reason why.
Sometimes yes. Cancer steals your body's energy, taking nutrition away from the rest of your tissues and most importantly your brain. This can lead to fatigue. Or, it could be the treatment; chemotherapy can definitely cause fatigue.