Where is the sugar?
When you freeze an aqueous sugar solution pure water freezes first, leaving a more concentrated solution until you reach the eutectic concentration. Only then does the sugar freeze along with the water to form a rwo-phase solid structure. If that structure is in the interior of the ice cube, likely since you cooled the solution from the outside, then licking the outside you got only the pure water "proeutectic" component. See https://en.wikipedia.org/wiki/Eutectic_system for more about this process.