The cuegle is a monster in Cantabrian folklore.
The image of El Cuegle eating a child is based on the actual painting, "Saturn Devouring His Son", by Spanish artist, Francisco Goya.
This episode opens with a quote from John Dryden's translation of Virgil's Aeneid: "Foretold our fate, by the gods' decree, all heard and none believed the prophecy."
The opening quote refers to Cassandra who in mythology had the ability to see the future but was never believed. The victim's address is on Cassandra Street. Also, someone who reads signs to divine the future is called an Augur and the baby's name is Auggie. In the first scene in the nursery the baby's name on the wall was August. It changed to Auggie in the scene where monster is taking the baby.
In usual Grimm fashion, the episode number features few times. The Malers live at 604 NE Cassandra Street (shown during the internet search for babies). The newspaper Renard is reading is vol. 604 (season and episode), issue 115 for the total number of episodes. The suspect's flat is 64, again for season and episode.