The wing as it moves through the air has two components of drag:
induced drag - is the drag which results from the fact that the wing produces lift. There will always be a component of induced drag. It is impossible (even theoretically) to design a wing which would have 0 induced drag.
parasitic drag - is the drag resulting from everything else - designers strive to reduce this.
Now as the plane moves through the air the power is simply P=f*v (force to overcome induced drag * velocity). The fact that neither the kinetic nor potential energy of the aircraft are changing makes no difference. (In reality - as the plane 'ploughs' through the air the air molecules will be accelerated - heated - hence their kinetic energy is increasing).
So what is the magnitude of this induced drag? I think, assuming some kind of 'ideal' wing, that the power expended to overcome induced drag will be be equal to the power required to overcome the constant accelerating force of gravity on the plane. I guess we could try to imagine this as the wing 'deflecting' a certain mass of air downwards. The mass of this air * the acceleration (i.e. force) will need to be equal to the force exerted on the aircraft by gravity - 9.8 N/kg.
Regards,
Gregory