piece of cake vs child's play

piece of cake and child's play both are nouns.

Word	Noun	Adjective	Verb	Adverb
piece of cake	Yes	No	No	No
child's play	Yes	No	No	No

As nouns, piece of cake and child's play are synonyms defined as:

Other synonyms of piece of cake include breeze, cinch, duck soup, picnic, pushover, snap, walkover.

piece of cake (noun)	child's play (noun)
any undertaking that is easy to do	any undertaking that is easy to do
	activity by children that is guided more by imagination than by fixed rules