Preheat your oven to 350°F (175°C). Grease and flour a baking pan.
In a large bowl, mix the grated carrots, sugar, and vegetable oil.
Add the eggs one at a time, beating well after each addition.
In another bowl, combine the flour, baking powder, baking soda, and cinnamon. Gradually add to the carrot mixture, mixing until just combined.
Pour the batter into the prepared pan and bake for 25 minutes or until a toothpick inserted into the center comes out clean. Let the cake cool completely.
In a mixing bowl, beat the cream cheese and butter until smooth. Gradually add the powdered sugar and vanilla extract, beating until smooth and creamy.
Crumble the cooled cake into a large bowl. Add the frosting and mix until well combined.
Shape the mixture into small balls and insert a lollipop stick into each one. Chill in the refrigerator for at least 1 hour before serving.