I have seen it made 2 ways...Cooked isomalt which is hard candy and of course royal icing...Check out some youtube videos and see if they show any...The isomalt has to be boiled to candy consistency and then poured over ice cubes to form the coral...when the heat hits the ice it hardens the candy.
I made mine out of Isomalt. I put ice in a big metal bowl and poured it over the ice and waited for it to harden. Took a knife and stabbed the coral because I needed small coral. I posted a pic of it with my Spongebob cake. message me if you have any questions. 
There is also a way of doing it using Royal icing you 'cook' in the microwave.
There is also a way of doing it using Royal icing you 'cook' in the microwave.
May I ask, how can you make corals with royal icing? I'd love to know 
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