いきましょう / will go

いきます

this is the masu-form of "go".

いき＋ましょう

Keep the masu-form stem "いき", and change the ending to "ましょう".

いきましょう

this means "go" with willingly accepting invitation by other.

いっしょに　かふぇに　いきませんか？

This means "Shall we go to cafe together?". And you are asked this, and you accept this invitation and want to say "will go!" in a way in which your attitude is like "Yes! let's go. I agree.". So, you say...

いきましょう