The defendant also admitted a number of other offences, including purchasing a shotgun without a certificate, possession of a shotgun with intent to endanger life and possession of a kitchen knife in a public place.
The bodies of Juliana Falcon, 48, Giselle Prosper, 13, and Kyle Prosper, 16, were found at a flat in Leabank, off Wauluds Bank Drive, on September 13 2024.
Nicholas Prosper, of Leabank, appeared in the dock at Luton Crown Court on Monday and spoke to confirm his identity and to plead guilty to three counts of murder.
Judge Michael Simon told the defendant his sentencing will take place on March 5 and remanded him into custody.
A 19-year-old man has pleaded guilty to the murders of his mother and two siblings in Luton.
