As Jocko says, drag force is proportional to speed squared, drag power is proportional to speed cubed. Going faster needs more fuel as a rule.
The significant factor in which gear you use (and hence engine speed) is that the brake specific fuel consumption (BSFC), the fuel used to produce one kW.hr of energy at the wheels, generally improves with more load and less speed (up to a point).
The BSFC map below is an example of a car petrol engine.
The "road load" in 4th gear is shown dotted to give an example of where the engine runs as vehicle speed increases. Higher gears will show as curves above this example, lower gears will be below it.
The top line in bold is essentially the maximum torque curve at wide open throttle measured in brake mean effective pressure BMEP (Bar), this is in essence the torque per litre with a constant factor applied (Nm = 7.958 x BMEP x swept volume). BMEP alllows you to compare different engines directly, taking swept volume out of it.
The lines curving from top left down towards bottom right are constant power lines (see right hand axis). If you run a car at a given speed you need a fixed power, lets say 30kW. Follow the 30kW line up towards the left and you'll see that at for example 4000rpm (low gear) the BSFC is about 400 g/kW.hr.
If you use a higher gear and run the engine at say 3000rpm, the BSFC for 30kW is around 300 g/kW.hr, and at 2500rpm it is about 270 g/kW.hr
Thus you can see that for cruising at steady speed using a higher gear generally speaking puts the engine nearer the "eye" of the map and thus gives a lower amount of fuel needed to produce the required power (and thus energy).
If you go too far it can make it worse, but that tends to be at extreme low rpm and extreme load (torque). For a typical petrol engine it is usually not beneficial to run at high load much below around 1500-1750rpm (heat losses in the slow cycles means lower thermal efficiency), and at near full load (open throttle) the engine usually runs slightly rich so fuel efficiency reduces.