Octane & energy density (heat of combustion) are completely independant of one another. eg methanol has a very high octane but only half the energy content of petrol. Energy density comes from the bonds present in the fuel. Carbon-carbon bonds liberate the most energy from a hydrocarbon when broken & reformed into carbon-oxygen bonds. Double bonds liberate more energy than single bonds. Carbon-hydrogen bonds liberate much less energy. The cheapest way oil companies raise octane is to add ethanol which will decrease energy density. The more expensive method is to add branched chain hydrocarbons (iso-octane etc) which contain a similar amount of C-C and C-H bonds so energy density will be similar. There are other ways of increasing octane with organo-metal compounds like tetra-ethyl lead and various other compounds. Again, no increase in energy density. Any oxygenated fuel eg ethanol, methanol has lower energy density.

Octane is a measure of resistance to detonation determined on a knock engine. Detonation is uncontrolled ignition in the engine ie. it's not spark initiated. There are several different octane rating scales. Research Octane Number, Motor Octane Number, R+M/2. MON is the best as it measures an engine under load. RON is the worst as it is measured on an unloaded engine. The US uses R+M/2, we use RON. There is often a 6-10 point difference between MON & RON, referred to as the fuel sensitivity