I'll give you a head start.
Yes, the power and therefore the kCals requirement for motion is greater if you ride the mile faster.
But, the windchill you experience negates the difference.
It is worst of all in a cool sidewind. Most rides are of generally circular route ( start and finish at the same place ) so this is the average of what you'll get all day.
Riding at 10 mph takes 6 minutes to cover the mile whereas riding at 20 mph takes 3 minutes. The total Cals required for Tractive motion is roughly 3 times at 20 mph as it is at 10 mph.
Windchill and heat wasted keeping damp clothes warm however, can be an equal or greater drain on the body as the Tractive effort – a 5 mph sidewind can be 2 kCals/min.
So at 10 mph, you're out in the breeze for 6 minutes and at 20 mph, 3 minutes.
So all in all, at 10 mph;
( 1.5 kCals/min x 6 ) + ( 2.0 kCals/min x 6 ) = 21
At 20 mph;
( 4.5 kCals/min x 3 ) + ( 2.0 kCals/min x 3 ) = 19.5
This is just one example where riding faster is more efficient than riding slower.
Do some more sums and you'll find an optimum speed for efficiency dependent on the meteorological conditions on the day.
This is one reason I don't dawdle along AUK 100s in the cool.