>>96162689
All we know is Perturabo NEEDED to become a Daemon Prince, as his soul was wounded by Fulgrim when he stole a part of it to fuel his own ascension. It is so implied in Slaves to Darkness by nurgle's emissary.
Headcanon time:
Perturabo didn't beat Angron into submission. He knew he was invincible. But Perty could control how he'd lose.
He fought Angron, bled him and was bled by him here and there. Some blood here, a bit more there. Until he made a blood circle on the ground. He then just convinced Angron ("let's bleed together and be brothers" - After De'Shea) to bleed on Terra, where it mattered.

The Iron Cage was the same. The fortress was "empty" because it was actually a giant summoning circle. Foundations salted with Istvaanian ash, drowned in brothers' blood.
With Dorn at the very center.