Nicholas Prosper, 19, appeared at Luton Crown Court over the deaths of Juliana Falcon, 48, Giselle Prosper, 13, and Kyle Prosper, 16.
Prosper 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.
A 19-year-old man has pleaded guilty to murdering his mother and two younger teenage siblings in Luton last year.
As he appeared in court on Monday, he spoke to confirm his identity and to plead guilty to three counts of murder.
Their bodies were found at a flat in Leabank, off Wauluds Bank Drive, in September.
