With all persons shall can be used to emphasisSpecial importance or attention given to something. E.g.: All I wanna do is have some fun.e something which the speaker feels certain to happen or wants to happen.

I shall definitely give up smoking this year!
We shall win!
"We shall overcome!"

To express offers, usually the auxiliariesA helping verb used with main verbs to express mood, voice and tense. E.g.: I can't stand when I am disturbed. ("can", "am") of permission, possibility, suggestion and willingness are used.

Shall can be used with all persons in formalNot belonging to colloquial or everyday speech; official. E.g.: I demand that Mr Smith call the person on whom the committee has decided. rules and regulations:

"Thou shalt not kill." (archaic form!)
Members shall enter the names of their guests in the book provided.

We could go and have a beer somewhere downtown.
Let's dance.
Let me help you.
Shall we throw a party sometime next week?
Shouldn't we have a pizza instead?