Kogan was born in New York City to author and Photographer Deborah Copaken Kogan and Russian-born child actor Paul Kogan. Paul emigrated from Moscow, Russia (then in the Soviet Union). Kogan has two younger siblings; a sister, Sasha (born March 1997) and a brother, Leo (born May 2006). His mother's family were Jewish immigrants from Russia, Ukraine and Lithuania and his father is of Jewish and ethnic Russian background. He considers himself Jewish and an atheist.
He attended the Dalton School in New York City during which time he was the lead singer/guitarist in a band, Flake, which released a self-titled EP in 2008. Before starring in Joshua, Kogan was a regular on the comedy series, Wonder Showzen. He had a supporting role in Lifelines by writer/director Rob Margolies. The film was released on April 3, 2009 at the Quad Theater in Manhattan after being shown at film festivals in the previous year. He also had a supporting role in the television series Delocated as David. He guest-starred on Law & Order: Special Victims Unit in 2011 in the episode "Blood Brothers" as Tripp Raines. His most recent acting role to date was Luca Jameson in the science fiction series The Tomorrow People.
