Preheat oven to 350 degrees Fahrenheit. Spray a mini Bundt pan with cooking spray and set aside.

In a large bowl, combine sugar and oil. Add eggs, flour, coconut, carrots, baking soda, cinnamon, salt, vanilla extract, and mandarin oranges (including the syrup). Mix to form a batter. Pour into the prepared pan.

Bake 30 minutes, until a toothpick inserted in the center comes out clean. Let cool 10 minutes in the pan before transferring cakes to a wire rack to cool completely.

In a bowl, beat the butter until creamy. Add cream cheese and vanilla extract and beat to combine. Add confectioners’ sugar, about a cup at a time, beating to incorporate after each addition.

In a piping bag fitted with a decorating tip (or in a plastic sandwich bag with the corner cut off), pipe frosting onto cooled cakes and sprinkle with toasted coconut flakes.