Nicholas Prosper, 19, pleads guilty to murdering Juliana Falcon, 48, Giselle Prosper, 13, and Kyle Prosper, 16.
Prosper had also planned to commit a shooting at a local school and a loaded shotgun with more than 30 cartridges was found hidden in a bush after his arrest, Bedfordshire police said.
Prosper murdered his family in a “cold-blooded attack” with a shotgun he obtained without a licence, said Chris Derrick, a deputy chief crown prosecutor at the Crown Prosecution Service.
Assistant chief constable John Murphy of Bedfordshire police said Prosper had intended to cause “maximum harm and distress” to the wider community.
DCI Sam Khanna, from the Bedfordshire, Cambridgeshire and Hertfordshire major crime unit, said: “This was a truly tragic and shocking case in which three innocent members of the same family have been brutally killed by their son and brother.