Where is the sugar?
When you freeze a dilute aqueous sugar solution pure water freezes first, leaving a more concentrated solution until you reach a high concentration of sugar called the eutectic concentration. Now you have the pure water that's frozen out, called proeutectic water, and the concentrated eutectic sugar solution from which the sugar is finally ready to freeze along with the water. Upon freezing this eutectic composition forms a two-phase eutectic mixture, in which the sugar may appear as veins or lamellae (like veins of some ores among Earth's rocks, though these typically form form a different process). 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.