Arrange 2 oven racks in upper and lower 1/3 of oven. Heat oven to 350°F. Spray 24 regular-size muffin cups with cooking spray, or line with paper cups. In large mixing bowl, combine flour, baking powder, baking soda and salt; blend well. In food processor or blender, combine beans, butter and 2 cups of the sugar. Cover; process 30 seconds or until smooth. Add eggs and egg whites. Cover; process 10 seconds. Add buttermilk and vanilla. Cover; process 10 seconds. Pour bean mixture into dry ingredients. Beat with electric mixer on low speed until moistened. Beat at medium speed 2 minutes. Fill each muffin cup about 3/4 full (reserve small amount of batter). Press 1 raspberry in center of each cup. Using remaining batter, spoon about 1 tsp of batter to cover each raspberry. Bake 17 to 20 minutes or until toothpick inserted near center comes out clean, rotating pans half way through for even baking. Cool 10 minutes in pan. Remove to wire cooling racks. Cool completely, about 20 minutes.
Meanwhile, in 1-quart saucepan, mix remaining 1 cup raspberries, remaining 1/4 cup sugar and lemon juice. Heat over medium heat until raspberries soften and release their juices. Press mixture through a fine mesh sieve. Discard seeds. Cool mixture.
In medium bowl, mix powdered sugar, corn syrup, cream and remaining 1/2 teaspoon vanilla. Beat with electric mixer on low speed until mixed. Beat on medium speed until thick and creamy. Remove papers from cupcakes. Frost cooled cupcakes, letting frosting drip over edges. When ready to serve, place cupcakes on dessert plates. Top with raspberry sauce.