I'm not so sure about running, but I know with water sports the power required to maintain a speed varies with the cube of the speed - ie double speed needs 8x the power. As the time taken will be 1/2, that still means you use 4x the energy to cover the same distance twice as fast.
Most of this comes from friction, which is the main resistance in water sports. In running, air doesn't offer nearly so much resistance so the energy use is more likely to be dominated by other (more constant?) factors.
From the journal of exercise physiology, this
article:
From a metabolic perspective, the primary finding of this investigation was a constancy of the metabolic cost per distance (MBTC) to changes in running speed, which is in agreement with previous studies (1,2,3). The running speeds used in our study ranged from 2.33 m/s to 4.0 m/s which was within the range of speeds collectively examined in previous research (1,2,3)