In addition to obvious and very good answers based on the fact that the blood is actually the thing which distributes energy throughout the body in form of lipids and sugars, You can, if You will, go more wacky. Let's see (pardon my tongue in cheek tone, would you? ;) )...
1. The vampire consumes the victim's soul along with the blood.
First, we have to assume that a soul actually carries some free energy. Since it takes between 15 to infinity years to create an adult human (sadly, most people never really develop) and throughout all those years a LOT of energy is consumed by the brain - which in turn is the machinery in which the software called soul resides - i think it's a safe assumption. Further more, we can bring up an old STEM joke: Exam question: Is hell exo or endo thermic?
Having been convinced that soul carries some thermodynamically usefull energy, we are now safe to say that a vampire with ability to devour it along with blood could get energy it needs from it. And think about all the other ploot hooks this brings!
PROS: Lots of possible plot hooks.
CONS: You can end up with a bit too many voices in Your head if You retain those souls and dont devour them completely.
2. In far cyberpunk dystopian gloomy raining future, humanity has perfected and miniaturized fusion reactors to pocket sizes - and vampires use them.
So, the basic idea is that all the energy calculations presented in other answers assume your normal average door-to-door biochemistry. But there is a loot of room down there, and lot of energy too. 790
If You'd care to check, You'd find that biomolecules contain a LOT of hydrogen. So, screw normal biochemistry, trash glycolysis and throw mitochondria to a bin of history. Your vampire has a biochemical cycle which rips any and all hydrogen atoms it can find in Your food and provides them to a miniature fusion reactor in your chest, which produces all the energy You'll ever need.
PROS: You're cyber-vampire-tony-stark
CONS: Staking You could trigger a nuclear meltdown? Hm, maybe that's a pro too...
3. Thanks to combination of really eldritch, ancient astral magic and possibly some Quantum Field Theory You either have magnetic monopoles or naked singularities in a catalytic center of a digestive enzyme
Fusion is nice, but let's go for E=mc^2. By a combination of exotic physics and magic You literally turn ALL matter of the blood You've drank into energy. Just like that, a molecule comes in, a lot of very very energetic gamma photons come out, then You just harvest them.
PROS: You are better than sun in terms of energy production efficiency.
PROS: You probably could shoot gamma rays
CONS: A horde of physicists stalks You all the time to make measurements and possibly kidnap You and make their lab rat
CONS: You leak photons. A real lot of them. You're sparkling. 227