Break the candy canes into several smaller pieces each. Combine the broken candy canes, sugar and water in a small saucepan over medium-high heat and stir occasionally until all of the sugar has dissolved.
Bring the mixture to a boil, then reduce and simmer, stirring frequently, for 5-10 minutes, or until all of the candy cane pieces have dissolved. Frequent stirring will ensure that the candy cane pieces dissolve more readily and don't stick to the bottom of the pan. USE CAUTION when stirring bubbling syrup to avoid burns.
Once fully dissolved, remove the saucepan from the heat and allow the syrup to cool. Once the syrup is room temperature, pour it into a glass bottle or jar and store in the refrigerator for up to two weeks.