Preheat oven to 350 degrees F. Butter two 8” round cake pans and line 8 muffin cups.
Whisk together flour, baking soda, baking powder, salt, and cinnamon together in a large bowl. Add in carrots and nuts.
Whisk together eggs, olive oil, milk, vanilla, and sugars in a medium bowl. Add this mixture to the flour mixture and stir until just combined.
Transfer 3 1/2 cups of batter to each cake pan and divide the rest among the lined muffin pan. Bake the cakes for 35-40 minutes and the cupcakes for 20 minutes, until a toothpick inserted in the center comes out clean. Cool the cakes and cupcakes on a wire rack.