With just sugar, you wouldn't be making beer, since malted grain is a key ingredient. It would be closer to mead, and like mead, the resulting drink would have no head since that's created by protein, which there is none in sugar. There would also be no residual sweetness or any other flavoring other than the alcohol, so it would taste pretty bad. You can add yeast nutrients just as when making mead to provide the free-amino nitrogen and other trace elements required to reduce any fermentation off flavors, but due to the lack of any real flavor in the ingredients and residual sweetness it would not taste good if you let it ferment out completely.
In Norway, and I believe in most of Scandinavia, some people make a low-alcohol drink that is water, sugar, yeast and optionally a little flavoring, such as a few raisins or some apple juice. This is called sukkerøl - sugarbeer. The trick with this is to let it ferment at room temperature just enough to produce the carbon dioxide required, and then the beers are stored in a cool cellar/fridge to almost halt fermentation. By stopping the fermentation early, there is still some unfermented sugar, giving some sweetness to the beer. It's important to chill the beers after a couple of days of fermentation or all the sugar will ferment out, producing a bitter, harsh tasting drink, and also the risk of bottle explosions.