Measure out raspberries and leave on counter. Preheat oven to 350°F Line a 12-cup muffin pan with paper cups or spray with oil.
Stir flour with cocoa, baking powder, baking soda and salt in a large bowl. Puree beets in a blender or food processor. Beat sugar with oil in a medium-sized bowl, using an electric mixer, until combined, 2 minute Beat in egg, then beets and vanilla. Gradually beat in one-third of flour mixture just until blended, then half of buttermilk. Repeat additions, ending with flour mixture. Divide batter among muffin cups, filling each 3/4 full.
Bake in centre of oven until a cake tester inserted in cupcakes comes out clean, 20 to 25 minute Cool in pan on a rack for 15 min, then remove cakes to a rack to cool completely before icing.
PUSH raspberries through a sieve into a bowl, using the bottom of a ladle. Discard seeds. Stir in cream cheese and icing sugar until evenly mixed. Spread over cooled cupcakes.