Cubit was the head football coach at the University of Illinois at Urbana–Champaign, first on an interim basis in the 2015 season and then promoted to the post full-time before his dismissal on March 5, 2016.
While at Delaware, Cubit played wide receiver and quarterback for the Blue Hens football team under head coach Tubby Raymond, earning Associated Press All-America honorable mention in 1974.
[18] Cubit's playing career ended with the 1974 NCAA Division II Football Championship game as the Blue Hens fell to the Central Michigan Chippewas by a score of 54–14.
As a high school coach, Cubit compiled a nine-year record of 79–15–2 at three different programs, Martin County, Academy Park and his alma mater Sharon Hill.
Cubit was named head football coach at Western Michigan on December 4, 2004, succeeding Gary Darnell.
After a nine-win season in 2008, Cubit lead Western Michigan to the Texas Bowl against Rice, where the Broncos lost, 38–14.
Following the 2011 season, the Cubit and Broncos participated in the 2011 Little Caesars Pizza Bowl, where they fell to Purdue in the final minutes by a score of 37–32.
During the course of his career at Western, Cubit has led the Broncos to upset road victories over Automatic Qualifying conference opponents Virginia (2006), Iowa (2007), Illinois (2008), and Connecticut (2011).
[22] The win made Western Michigan 2–0 all-time against Iowa, having previously upset the Hawkeyes at Kinnick Stadium in 2000.
[23] Western Michigan concluded the 2007 season with a victory at home against Temple, then carried that momentum to a program-best 9–4 record in 2008.
[26][27] On December 17, 2012, Western Illinois publicly acknowledged that Cubit had voluntarily withdrawn his name from consideration.
On January 14, 2013, Cubit was hired by the University of Illinois as the team's offensive coordinator and quarterbacks coach, replacing co-coordinators Chris Beatty and Billy Gonzales.
[32][33] On August 28, 2015, Cubit was named interim head coach at Illinois for the 2015 season after the university fired Tim Beckman for alleged mistreatment of players.
[34][35] On November 28, 2015, Illinois removed the interim tag and named Cubit as its 24th head coach, giving him a two-year, $2.4 million contract.
"[1] He was replaced by former Chicago Bears and Tampa Bay Buccaneers head coach, Lovie Smith.
In 2017, Cubit returned to Martin County High School in Stuart, Florida to serve as the head football coach, reprising a role he held for three seasons between 1986 and 1988.