Does sugar give moisture?
Sugar helps with moisture content and its mobility in baked goods.  Every industrial sliced bread has sugar as a major ingredient. It is there to slow down staling. It's not clear how it does it, but sugar seems to impede the modification of starch and the flow of moisture to gluten. Sugar also helps breads retain more moisture. This very obvious among breads, but it applies to cakes, which are breads with added fat and sugar.