The team plays at the Liberty Memorial Coliseum (also known as Bush Stadium) in Staunton Island. They also have an official fan club whose main building is right across the stadium. Many Cocks fans can be seen walking around the Bush Stadium and some can even be heard asking others if they are a fan of the Liberty City Beavers (their fierce rivals). The Cocks and the Beavers have known meetings, implying that there is a fierce rivalry/derby. On The Tight End Zone, a program on West Coast Talk Radio, Derrick Thackery mentions a match between the two. The second occurs in September 2001, with the Cocks beating the Beavers 3-0.
Oddly, despite the fact that the team crest and rivalry with the Beavers, plus an article from Liberty Tree, all show that they are a soccer team, the field inside the stadium and the "Two-Hand Toss" mission suggests that they play American football. This may be an oversight by Rockstar, however it is possible that the Cocks also field a football team; this is somewhat akin to the New York Giants, who shared an association with the MLB's New York Giants. Additionally, there was an American football team called the New York Yankees in the 1940s, who were owned by Dan Topping, a former part-owner of the MLB's New York Yankees.
There are still many references to the LC Cocks in the HD Universe. Eduard Borodin was visiting Liberty City to purchase the team according to an Liberty Tree internet article after the mission Paper Trail. Theres also an LC Cocks book in Luis' Apartment in The Ballad of Gay Tony. Presumably, they share a rivalry with the Liberty City Beavers as well as Red Mist XI.
- Another one of Rockstar's crude humorous jokes, the word "cock" can mean a rooster, or (more likely) a penis.
- The team is likely based on the New York Cosmos, as the logo for the Cocks is similar to that of the Cosmos.
- Additionally, the logo for the Cocks contains 14 stars; in real-life, stars on a team's crest would signify the number of championships a team has won; this would imply that the Cocks are quite successful, possibly explaining their popularity in Liberty City.
- Carl from GTA III is a notable Cocks fan.
- Michael Hunt, the DJ of Head Radio, is a noted fan of both the Cocks and its rival team, the Beavers.
- The same can be said about their stadium name, Bush Stadium, which can mean a plant, or pubic hairs. It could also be a reference to the Bush family.
- An outfit named as the Cox Mascot Outfit can be rewarded to the player in Grand Theft Auto: Liberty City Stories after the completion of Slash TV. This suggests that the term Cox is either a colloquial term for the team or the name of their mascot.
- Bush Stadium is similar to Autzen Stadium in Eugene, Oregon, though the stadium is much more similar to the Los Angeles Memorial Coliseum. The civil rivalry between fans of the Cocks and Beavers is similar to the civil rivalry of University of Oregon Ducks (Liberty City Cocks) and the Oregon State University Beavers (Liberty City Beavers).
- The rivalry between the Cocks and the Beavers could also be a reference to the infamous Portland Timbers–Seattle Sounders rivalry, which is considered the most intense and hostile soccer derby in the United States.