Heat sugar, butter, water, coffee, and chocolate in a 3-quart saucepan over low heat, stirring constantly, until chocolate is melted and mixture is smooth; remove from heat. Beat eggs in a separate bowl; gradually pour in the chocolate mixture, whisking constantly. The batter will be very thin. Transfer batter to prepared pan. Bake in the preheated oven until a wooden pick inserted in center comes out clean, about 45 to 50 minutes. Cool completely. Remove sides of pan.