child's play vs piece of cake

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

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

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

Other synonyms of child's play include breeze, cinch, duck soup, picnic, pushover, snap, walkover.

child's play (noun)	piece of cake (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