cane vs beat up

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

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

As verbs, beat up is a hypernym of cane; that is, beat up is a word with a broader meaning than cane:

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

Other hypernyms of cane include beat, work over.

cane (noun)	beat up (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

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