subject verb agreement - He is one of the men who do/does the work

Let us say, I have been given two sentences in an MCQ test and I need to pick up the correct one.

• He is one of the men who do the work.


• He is one of the men who does the work.

Somehow, I lean towards the second one ("It is I who am to blame", the one sentence memorized to take care of cases like this), but I have found some grammar books supporting the first one.