In a large pot, mix sugar, corn syrup and water. Cook over a medium-high heat, while stirring until the mixture comes to a boil.
Clip candy thermometer to the pan. Continue cooking over medium-high heat without stirring until it reaches 260 degrees (hard-ball stage).
While the sugar mixture is boiling,beat egg whites in a large bowl on a medium speed until they form stiff peaks, when pushed with a spoon.
Gradually pour the hot sugar mixture in a thin stream over the egg whites, while the mixer is still set on medium. After all of the hot mixture has been added to the egg whites, increase speed to high and beat for about 3 minutes.
Turn off mixer and scrape sides of bowl. Add vanilla. Continue beating on high until the candy starts to lose its gloss (about 5-6 minutes). When beaters are lifted, the candy should fall in a thick ribbon and form a mound.
Stir in candy cane pieces, then drop with a tablespoon onto wax paper.
Let them set until they have cooled and the outer layer has become somewhat dry and not sticky (12 hours). Store in an airtight container.