expression
shall I?; would you like me to?
Polite volitional form used to offer to do something for the listener. Often implies 'if it's okay with you' or 'shall I do it for you?'.
See also: ましょう
荷物を持ちましょうか。
Shall I carry your luggage?
expression
shall we?; let's (do something)
Polite volitional form used to suggest doing something together. Softer and more inviting than the plain volitional form.
そろそろ行きましょうか。
Shall we get going?