Coat 3 (8-inch) round cakepans with cooking spray. Line pans with wax paper. Coat wax paper with cooking spray. Set pans aside.
Beat butter at medium speed with an electric mixer until creamy; gradually add 3 cups sugar, beating well. Add sour cream; beat until light and creamy. Add eggs, 1 at a time, beating until blended after each addition.
Add flour alternately with milk, beginning and ending with flour. Beat mixture at low speed until blended after each addition. Stir in vanilla. Pour batter into prepared pans.
Bake at 350° for 27 to 30 minutes or until a wooden pick inserted in center comes out clean. Cool in pans on wire racks 10 minutes; remove from pans, and cool on wire racks.
When cake layers are completely cool, place peanut butter in a large mixing bowl. Place 1 cake layer on a cake plate.
Bring remaining 3 cups sugar and 1 1/2 cups water to a boil over medium heat in a heavy 2-quart saucepan, stirring gently until sugar dissolves. Using a pastry brush dipped in hot water, wash down any sugar crystals on sides of pan. Cook, without stirring, until a candy thermometer registers 234° (soft ball stage). Pour over peanut butter, and beat with a wooden spoon until blended and mixture thickens just slightly.
Immediately pour about 1 cup frosting over cake layer, spreading almost to edges. Quickly repeat procedure with second and third layers of cake and frosting. Quickly frost sides of cake with remaining frosting. Let cake stand at least until frosting is firm before cutting. (Cake will remain warm inside for about 2 hours.
Tips: Work rapidly to frost cake. Frosting will harden quickly. Use a long thin spatula dipped in hot water to help spread frosting when it begins to become firm. An electric knife works best to cut the cake if serving while still warm.