beat up vs cane

beat up is not a noun while cane is a noun.

Word	Noun	Adjective	Verb	Adverb
beat up	No	No	Yes	No
cane	Yes	No	Yes	No

As verbs, cane is a hyponym of beat up; that is, cane is a word with a more specific, narrower meaning than beat up:

beat up: give a beating to; subject to a beating, either as a punishment or as an act of aggression
cane: beat with a cane

beat up (noun)	cane (noun)
	a stiff switch, used to hit (usually students) as punishment
	a stick that people can lean on to help them walk
	a strong slender often flexible stem as of bamboos, reeds, rattans, or sugar cane

beat up (verb)	cane (verb)
gather	beat with a cane
give a beating to; subject to a beating, either as a punishment or as an act of aggression