Energy drinks aren't supposed to supply you with nutritional energy but to temporarily stimulate your mental and/or physical functions and encourage your body to use energy it already has. Such stimulated person might be seen as "more energetic" because of
enhanced alertness, awareness, wakefulness, endurance, productivity, and motivation, increased arousal, locomotion, heart rate, and blood pressure, and the perception of a diminished requirement for food and sleep.
(source of above description)
What are energy drinks made of:
Energy drinks can contain more than 15 ingredients, but the essential components come in five categories: (1) caffeine; (2) a sweetener of some kind (usually sugar); (3) one or more amino acids (most often taurine but sometimes L-carnitine); (4) vitamins B and (5) one or more plant/herbal extracts such as ginko biloba, guarana, ginseng, milk thistle etc.
(source)
In all energy drinks I've personally seen there was only one clearly stimulating compound and it was caffeine, "the world's most widely consumed psychoactive drug" (as Wikipedia nicely desbribes it).
Caffeine, an adenosine receptor antagonist, is a stimulant that can influence the activity of neuronal control pathways in the central and peripheral nervous systems. It is the most common stimulant in EBs [Energy Beverages] (...)
(Energy Beverages: Content and Safety, 2010)
There are also other substances in energy drinks, but their purpose and effect is often unclear. or example, glucuronolactone, ginseng, ginkgo biloba and many others. Some of them might actually work in some mildly stimulating way. If you're interested, read Energy Beverages: Content and Safety.
Now, sugar is not considered a stimulant, although
Administration of glucose or other carbohydrates before, during, and after prolonged exercise (>1 hour) has been shown to postpone fatigue, conserve muscle glycogen, and improve performance.
(Energy Beverages: Content and Safety, 2010)
There was a common myth about children being stimulated by candies and other sugar products, but it was proven false. In some aspects and for some people (e.g. elderly) sugar may improve some congnitive perfomance, but for others it (e.g. infants) it may work as sedative. Its removal from energy drink probably doesn't change much, other sweeteners are used instead, although one may wonder what are all those vitamins then:
Because EBs contain large amounts of sugar, these vitamins are touted as ingredients necessary to convert the added sugar to energy. Hence, the B vitamins are the “key” needed to unlock all the energy provided by the simple sugars in EBs, and this is the extra energy that EB companies claim their product can provide.
(Energy Beverages: Content and Safety, 2010)