What sounds better is what I do.
My mum, Pa, Auntie, 4 brothers, 6 sisters and 2 cousins all live with me.
My mum, Pa, Auntie, 4 brothers, 6 sisters and 2 cousins all live with I.
Also, you can use Grammarly to write correctly on an essay. Grammarly also does like the sentence 'My mum, Pa, Auntie, 4 brothers, 6 sisters and 2 cousins all live with I.' cause it's bad grammar.
I is a subject.
Me is an object.
The phrase "lived with ___" is a prepositional phrase, due to the preposition with.
The word that follows with is then the object of the preposition.
Since we want an object, we use me.
Side note: I is only used when the speaker is performing the action. Here, the subject (performer of the action) is "my mum, pa, auntie, 4 brothers, 6 sisters, and two cousins."