It seems castration is popularly favored as a method of punishment for raping a child, but less so as punishment for raping an adult. Do you agree? If so, why?

Castration is fine but frankly I think subjecting the rapist, in either case, to the same thing their victim was subjected to would be a good punishment. Let them experience the pain, violation, and feeling of being defiled that goes with rape. Should that prove ineffective and you have another worthless recidivist on your hands, simply shoot the bastard, there's already too many psychos who can't or won't try to better themselves in the world. If one has a rape fantasy, fine, but the moment it becomes reality you've crossed the line. So far as I am concerned rape, no matter the victim's age, is on the same level of murder, if not worse. With murder, when its done its done, the victim is freed of their pain and this twisted world. With rape the damage is something that can never be really undone, the victim is affected by it to some degree for the rest of their life. Some manage to move past it, for others it is something they never get over. It takes an act that should be the height of intimacy between a couple and degrades it into an abusive, vile thing in pursuit of power.

I know it seems like the perfect solution to many, but the fact is, not having genitals won't stop someone from raping again (and not all rapists are men, either). I read once about a girl being raped with a pair of chopsticks, castration wouldn't solve anything there.

I think it's good for both.

Wouldn't castration be under cruel and unusual punishment? Where exactly is this kind of punishment favored?