intellectual vs cerebral

intellectual is a noun but cerebral is not a noun.

Word	Noun	Adjective	Verb	Adverb
intellectual	Yes	Yes	No	No
cerebral	No	Yes	No	No

As adjectives, intellectual and cerebral are synonyms defined as:

intellectual and cerebral: involving intelligence rather than emotions or instinct

intellectual (noun)	cerebral (noun)
a person who uses the mind creatively

intellectual (adjective)	cerebral (adjective)
appealing to or using the intellect	involving intelligence rather than emotions or instinct
involving intelligence rather than emotions or instinct	of or relating to the cerebrum or brain
of or associated with or requiring the use of the mind