The group is alleged to have kidnapped brothers Damiro Cardenas Victoria and Anselmo Cardenas Victoria whose bodies were found April 19.
The adults are being held pending trial, and the minors were handed over to family and children’s authorities.
Meanwhile, police shot dead “el Zorro,” a supposed leader of the same cartel, in the town of Barbacoas, Narino, the prosecutor’s office said.
The Gulf Cartel was formed by paramilitaries who demobilised in 2006.