Are candy canes safe for cockatoos to eat?

No. The main reason why is because cockatoos are simply made of long wires and barbecue sauce. The sweetness of the candy cane would cancel out the wires and barbecue sauce, thus resulting in mad hallucinations, feces all over your brand new carpet (Stanley Steemers can't help you now), and repeatedly screaming "I WHIP MAH HAIR MACK AND FORTH".

If you have already given the candy cane to your cockatoo, I suggest getting earplugs and a pooper-scooper; it worked splendidly for me.