Can I marry my father's cousin brother's son?

You both will have the same surname and same gotra. As per the Hindu religion, such marriages are not allowed. Grandfather of you and grandfather of the boy are own brothers. So the relationship will come under Sapinda relation. But if there is no complaint to anybody and if both the families accept the marriage you may not have any problem. But legally it is not allowed.
Many doctors also don't suggest such marriages as the chances of some health problems for their children maybe more. But it is not always true that the children will have some problem. Both of you should sit together and discuss all the issues and then make a decision. Your families consent is very important. Otherwise, they can challenge the marriage in court.

By most customs where the patriarchal system is followed, this kind of marriage is not allowed and is considered as forbidden relationship as they are akin to brother-sister relation. This falls under the Sagothra or Sapinda relationship.

However in certain customs this may be allowed. If your family traditions and customs , the customs of the community or geography allow this kind of marriage then it may be possible. But the fact that you have asked this question hints that it is not permitted in your community/society.If so, your parents , relatives and well wishers will not accept this and you may have to face many problems ahead if you take some harsh an opposing decision.
Hence consult your parents,relatives and well wishers and take a decision which will not antagonise your people but will fetch their support.

The Hindu Marriage act prohibits marrying in near cousins falling under Sapinda relationships.
Counting from the boy or the girl as the first level, the Sapinda relationship extends as far as the third generation (inclusive) in the line of ascent through the mother, and the fifth (inclusive) in the line of ascent through the father, the line being traced upwards in each case from the person concerned.
So, keeping the above law in view you cannot go for this relationship. But in some communities this is allowed and if it is so then the legislation would not be applicable for them.
Many people are ignoring this legislation and going ahead with marriage in close relation also but it has some legal implications. For example, if tomorrow someone wants to take divorce or there is some property dispute and someone makes a complaint then all sorts of complications might arise at that point of time. One has to take a cautious and calculated approach in such matters.

Both of you cannot have the marriage alliance because of existence of close relationship between you and the boy falling under Sapinda Relationship. However, such a relationship is prevalent in some regions or customs. Hence living a society gracefully, you need to abide by the rules framed by the society.
However marriage between the close relationship invites some health issues arising out of alliance of the close relationship. This may manifest in the different forms such as Diabetes, High Blood Pressure, Heart Ailments etc. Both of you need to have a consultation with the genetic specialist to evaluate any possibility of contracting of genetic diseases.
In case of clearance from the medical side and the norms prevalent in your society, you can go ahead with the marriage. But before that take an appointment with a reputed lawyer for avoiding any legal complication as a result of such a marriage.

As per the Hindu marriage act, this kind of marriage is not allowed as It falls under the sapinda relationship. But, some communities allow this marriage. You should consult your family member because their acceptance is very important so that problems may not arise in future. Your marriage is also not acceptable from a biological point of view as there would be more possibility that a born baby with this relationship may have biological problems. Moreover, before making this alliance you should consider the legal point of view as legally it is not allowed. If any property related dispute happens in future then a problem may arise. Even after considering all these points, you are eager to have this relationship then take permission from both sides.

Your relationship is very close and it is not even legally possible to establish a marriage relationship. However, if you want, you can talk to your family, sometimes some family customs and social customs seem different. Some communities also follow local rules, so take a decision in this matter only after consulting your family and acquaintances. Marriage is a relationship that may bond two people but in actuality, its impact is found in both families and this is the reason to involve other members of your family in this discussion