The Demon Brothers are stated to be the Rulers of Devildom and the seven most powerful demons, but in practice what that means is that they're Diavolo's ministers.
Lucifer and Diavolo are co-Prime Ministers, since he hasn't ascended the throne yet, but Lucifer will be Prime Minister proper when Diavolo becomes king.
I haven't decided on them all, but Mammon runs the Ministry of Finance, Satan does Education, Asmo probably does foreign affairs or something.
The seven of them have held their posts for a REALLY long time, in addition to being the avatars of their various sins.
With how busy they get, it's inevitable that they get behind on current knowledge, but it wouldn't do for Devildom Rulers to be outdated.
So every few hundred years or so, they take a few years off work to attend RAD, which functions as a university.
There are other schools and academies dotted throughout the Devildom, but RAD is considered the most elite.
It is considered an honour for a demon to attend school with them, and their admissions process becomes very competitive when the demon brothers announce their enrolment.
Each sibling also attend school on their own sometimes, without the other brothers.
Satan has attended medical school multiple times and has the most number of doctorate degrees.
Asmodeus has several psychology degrees (and so does Mammon, ostensibly to help with gambling and other money related matters.
Levi is fluent in the most number of languages both dead and alive, mostly to consume more media.
Belphie attended culinary school once so he can feed Beel better.
Lucifer mostly studies law.
Mammon is a certified accountant, and very carefully logs every single financial transaction he makes, even the money he gets from selling stolen items and the money he lost from gambling.
Beel takes first aid courses often to keep his skills sharp.
