No. Thomas Jacob Black (aka Black Jack) was born to Judith Love (Cohen) and Thomas William Black, both satellite engineers. He is of British-German (father) and Russian Jewish (mother) ancestry.
Though Black's parents divorced when he was 10, he did say that he had a good childhood. "My parents were very supportive of me and my artistic endeavours. My father and mother came to every school play I ever did," he told The Guardian.
On the other hand, actor and filmmaker Jack Nicholson has five children - Jennifer from his only marriage, to actress Sandra Knight; Caleb whose mother is actress Susan Anspach; Honey the daughter of model Winnie Hollman and Lorraine and Raymond from his relationship with Rebecca Broussard.
Of interest, RantHollywood.com shares a list of celebs you didn't know are father and son.