Yes, there are multiple ways in fact.
There is one main cuck route, but also some cuckholding content in other routes:
The main cuck route is keeping Eric a beta-male, to do so, be nice and understanding to him early in the game so he accepts when you ask for an open relationship while he is gone to Somalia, after that choose red dialogue options when having cybersex with him (the ones where Ash talks about sleeping with other men), then just never break up with him and don't commit to any other things that could override your relationship with him (don't join a gang, don't get in a serious relationship with Eva or Dave).
There are no point requirements as far as I remember and the ammount of cuck content you get is based on what other relationships you manage to develop while cheating on Eric (the main ones you should try to shoot for are Tyrone, the rapper; and Arthur, Eric's father).
There's a cuck scene in the gang route as well, stay in a relationship with Eric when he leaves for Somalia, then join the gang (stay in touch with the gangbanger that harasses you right before Eric leaves, have 20+ bad points).
There's also minor cuck content if you have a relationship with your own dad while dating another man (you can have your dad's child and lie to your boyfriend that it was his). To get a relationship with your own dad you need to have a lot of good points (several checks during the game, first a 14+ one, then a 20+ one, then finally a 25+ one), help your dad recover from his depression, and have Ash develop an interest on incest.