Beat the first 6 ingredients at low speed with an electric mixer for 1 minute. Scrape down sides, and beat at medium speed 2 more minutes until well blended, stopping to scrape down sides, if needed. Pour batter evenly into 3 greased and floured 9-inch round cakepans.
Bake at 350° for 20 to 23 minutes or until cakes are light brown and spring back when lightly pressed with your finger.
Cool in pans on wire racks for 10 minutes. Remove from pans; cool completely on wire racks.
Place one layer on a serving platter. Spread with 1/2 cup blackberry jam, leaving a 1/2-inch border. Spread a smooth, thin layer of warm Quick Caramel Frosting over jam. Repeat layers. Top with third cake layer. Spread top and sides of cake with remaining Quick Caramel Frosting, working quickly before the frosting hardens. (If frosting becomes too hard to spread, place it over low heat for 1 minute, stirring constantly.) Let cake stand 10 minutes.
Note: For testing purposes only, we used Knott's Berry Farm Blackberry Jam.
Tennessee Jam Cake: Pour batter evenly into 2 (9-inch) round cakepans. Bake at 350° for 26 to 28 minutes or until cakes are light brown and spring back when pressed with your finger. Place one layer on a serving platter, and spread 1/2 cup of jam on top of layer. Spread warm Quick Caramel Frosting smoothly over jam. Top with remaining layer; proceed as directed.