That's what people always say. But I don't recall ever having seen it so straightforward in a scripture before:
Blessed be God, even the Father of our Lord Jesus Christ, the Father of mercies, and the God of all comfort;
Who comforteth us in all our tribulation, that we may be able to comfort them which are in any trouble, by the comfort wherewith we ourselves are comforted of God.
For as the sufferings of Christ abound in us, so our consolation also aboundeth by Christ.
And whether we be afflicted, it is for your consolation and salvation, which is effectual in the enduring of the same sufferings which we also suffer: or whether we be comforted, it is for your consolation and salvation.
2 Corinthians 1:3-6
In other words, Paul felt that when he was comforted, it was so that he could comfort those he served, and when he suffered, it was so that he could relate with those who suffered, and both so that he could better know Christ.