Yes candy canes do contain have xylitol in them so do not feed your dog any candy canes as it can cause a drop in blood sugar in the dog and lead to death if the dog is not treated.
However it's unlikely that if the dog got a small bite of a candy cane that they would be harmed but still do not feed dogs any candy canes just to be safe.
Different companies make candy canes and use different ingredients and it should say on the package whether or not a certain brand of candy canes contain the ingredient xylitol.
But if it doesn't say then do not give the dog any of those candy canes to avoid the dog getting sick.
Sugar Free candy canes usually do contain xylitol as the artificial sweetener which can be deadly to dogs.