At the beginning of the play, it seems like Cory is really trying to be like his father. Rose even points this out to Troy, saying, "He's just trying to be like you with the sports" (1.3.118). In one scene, we see Cory try over and over to engage his father in a conversation about baseball, but Troy constantly shoots him down. Later on in the play, we actually see Cory pick up Troy's bat and attempt to hit the rag ball in the front yard the way his father does. It's pretty ironic that Cory tries to be like his father by playing sports, because this is precisely the issue that tears them apart. (For more on that, check out Troy's "Character Analysis.")
Though Cory begins the play trying to be like his father, he ends it trying to escape him. We see Cory return home on the day of Troy's funeral wearing a Marine corporal's uniform. Stage directions tell us, "His posture is that of a military man, and his speech has a clipped sternness" (2.5.14). It definitely seems like Cory has been through a lot since Troy kicked him out seven years earlier. We learn in this scene that Cory plans to get married soon. It seems like he's definitely on the road to becoming his own man, but he's still haunted by his father. He tells Rose:
The whole time I was growing up...living in his house...Papa was like a shadow that followed you everywhere. It weighed on you and sunk into your flesh. It would wrap around you and lay there until you couldn't tell which one was you anymore....I've got to find a way to get rid of that shadow, Mama. (2.5.81)
At first, Cory tells his mother he's not going to Troy's funeral. He sees this as his last chance to "say no" to his father (1.5.79). Rose goes off on her son, saying that being disrespectful to his father isn't going to make him any more of a man. She advises her son, "That shadow wasn't nothing but you growing to yourself. You got to either grow into it or cut it down to fit you" (1.5.86). She continues, saying that she's trying to raise Raynell, Troy's illegitimate daughter, the same way Troy raised Cory: "I'm gonna give her the best of what's in me" (2.5.88).
In the end, we're given hope that Cory will be able to find some middle ground. It seems likely that he'll be able to take the good things his father taught him and, perhaps, leave the bad things behind. It could be that the violent cycle of father-son rivalry that began between Troy and his father and continued with Troy and Cory may just be over. This moment of hope comes when Cory and Raynell sing a song that Troy used to always sing about a dog named Blue. When the two sing "Blue laid down and died like a man / Now he's treeing possums in the Promised Land" it seems pretty clear that they're really singing about Troy (2.5.101). When Cory sings, "You know Blue was a good old dog," it seems he may be finding peace with the shadow of his father (2.5.97).