I always have used royal icing when decorating sugar cubes. However... I have never tried to dissolve them in hot beverages. We always placed the decorated sugar cubes among the plain sugar cubes.... and used the plain ones for the beverages. I will look forward to seeing if anyone else has done this differently. Kel
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Royal Icing

2 2/3 cups sifted powdered sugar
4 Tbsp. warm water
2 Tbsp. meringue powder
coloring (best to use cake decorating gel coloring) if using liquid colors, reduce the amount of warm water you use

Beat sugar, water, and powdered sugar in a medium bowl with electric mixer 7 to 10 minutes or until stiff. Spoon icing into a pastry bag(s) fitted with your choice of tip(s). Allow icing to harden. Store in an air-tight container.

One tip when handling Royal Icing, make sure all of your bowls, scrapers, etc. are completely oil/grease free. The slightest bit of oil will ruin your entire batch of icing. And, do not leave your unused icing exposed to the air -- keep it tightly covered with cellophane-type wrap. Royal icing can begin to harden very quickly.