Corporal punishment is legal in public schools in 19 states, primarily in the South. It’s possible that corporal punishment of criminals is considered “cruel and unusual punishment.” In any case, in Ingraham v. Wright (1977), SCOTUS said corporal punishment of students wasn’t a violation of “cruel and unusual punishment” because that clause only applies to criminals.
ZD, I think you’re wrong about caning for littering in Singapore. Caning is used as a punishment for a variety of crimes from rape to vandalism to hiring illegal immigrants, but as far as I can determine, not for littering.