Place rack in the center of the oven and preheat to 350 degrees. Generously grease and flour 2 round 9-inch cake pans.
Place cake mix, sour cream, water, oil, food coloring, eggs and vanilla in a large mixing bowl. Blend with an electric mixer on low speed for 1 minute.
Scrape sides of the bowl with a rubber spatula and beat for 2 to 3 more minutes on medium speed. Divide the batter between the two pans, smoothing it out with the spatula. Place pans in oven side by side.
Bake the cakes until they spring back when lightly press with your finger and just start to pull away from the sides of the pan, 28-30 minutes. Remove pans from oven and place on wire rack to cool for 10 minutes.
Run a dinner knife around the edge of each layer and invert each layer on a rack, then invert them again on another rack so that the cakes are right side up. Allow to cool completely, 30 minutes more.
Prepare the frosting. Place one cake layer on serving plate, right side up. Spread the top with frosting. Place second layer on first layer right side up and frost the top and sides of the cake with clean, smooth strokes.
Place cake uncovered in the refrigerator until the frosting sets, about 20 minutes. Store in refrigerator for up to 1 week.
Place cream cheese and butter in a bowl. Allow to come to room temperature. Beat with an electric mixer on low speed. Stop the machine and gradually add confectioners' sugar, running the machine on low speed until mixture becomes spreadable. Fold in vanilla. Use immediately.