OK, lets examine this very carefull shall we?
Christs Cup of Suffering refers to Him bearing the Agony and suffering of all sins that men deserve, this is done on the Cross. When Jesus stated that they will be baptized and drink of the Cup you have taken it out of context. Try reading it carefully, it clearly states that they will be Baptized with Him and drink the Cup with Him. When one calls upon the Lord for Salvation they are Baptized into His Body or the Church and they partake in His cup which signifies that one must be obedient unto death, this in no way states that they will bear the same agony as Him. Think about it!
God Bless!