I'll try to sum this up.
From what we have seen in Alien 3, xenomorphs do eat.
As Daveberg pointed out, it could be a sign of aggression, but if this were to be true then I fail to understand why the xenomorph would openly consume its food rather than attack the corpse with its inner jaw or its claws. It also would not explain why the xenomorph would go through the risk of committing such an act when other dangers were still present.
However, we clearly can see it consuming its prey, which means that the food must be going somewhere. In turn, this points to the possibility of a digestive system.
Xenomorphs take on the traits of their hosts. It is possible that they adopt aspects of their host's internal organs. Thus, a xenomorph could easily have a digestive system.
We never saw the xenomorph in Alien eat, but we also did not see the corpses. In the deleted scenes we did witness the xenomorph converting its victims into eggs, which would give it reason not to feed.
In Aliens, we never saw the xenomorphs eat, but we also never saw what happened to their hosts after they died. Considering that the xenomorphs are highly efficient creatures, it seems most likely that they eat the deceased hosts for sustenance after they are no longer of use.
When we witnessed Alien: Resurrection, we never saw what happened to several members of the crew. It is highly likely that they have been consumed as well.
Typically, when an organism functions, it expends energy. It also needs to take in energy in order to meet this cost. That is why they have to eat.
If there was no food, the xenomorphs would not consume one another, but enter a form of suspended animation (hibernation) until more prey presents itself. This was witnessed in Aliens, when no xenomorphs were initially seen. Instead, the hive was gradually roused as the marines maintained their presence.
A xenomorph certainly could eat another xenomorph. Their entire bodies are resistant to the acidic blood which their species possesses. But I doubt there would ever be an incident where this would be entirely necessary.
And thus I clothe my naked villainy
With old odd ends stolen forth from holy writ
And seem a saint when most I play the devil.