Band's profits

There are many options. Usually the members decide upon at the begining. they can evenly share the revenues or decide other way.

For example, royalties may be divided according to composition\ mastering, (For example: Composer get the  royalties of the composition, and all the members evenlly share the rest of the royalties.

I dont know how exactly did the the beatles share their cake. 

Yes, wsosfr is right. Legally the royalties go to the person or the people who wrote the lyrics and the music, but in many bands the writes share them with other members. There are opposite cases too, I think the former members of The Smiths had a trial over royalties.

In terms of Independent or Non-incorporated artists, a bank account is set up in the name of the band; DBA [Doing Business As] - The Band Name.

 Each member typically has equal access to this account and it is used for band related expenses, as well as to deposit profits from merchandise sales, CD Sales, and performance revenue.

Payments from all of these profit revenues are deposited in the account and only withdrawn for band related expenses.

 However, this is only the case until the band is picked up or signed to a label, in which it becomes a lot more complicated, as was alluded to above [i.e. Royalties go to song writer / composer].

I do not know how the Beatles profit margins were divided, however in most cases individual shares of the profit are contracted at the beginning of a bands relationship; either the relationship between each other, or the relationship with their respective label.

It will depend on a group band and management but mostly the most higher paid was the lead vocalist and followed by lead guitarist...