sum vs sum up

sum is a noun but sum up is not a noun.

Word	Noun	Adjective	Verb	Adverb
sum	Yes	No	Yes	No
sum up	No	No	Yes	No

As verbs, sum and sum up are synonyms defined as:

Other synonyms of sum include add, add together, add up, summate, tally, tot, tot up, total, tote up.

As verbs, sum and sum up are synonyms defined as:

Other synonyms of sum include summarise, summarize.

sum (noun)	sum up (noun)
the whole amount
the choicest or most essential or most vital part of some idea or experience
a quantity obtained by the addition of a group of numbers
the final aggregate
a set containing all and only the members of two or more given sets
a quantity of money