Preheat oven to 325 degrees F (165 degrees C). Lightly grease and flour three 9-inch round cake pans. In a medium bowl combine the flour, baking soda, baking powder, cinnamon, white sugar, and salt. Mix well. In another bowl, beat eggs, vegetable oil, and 1 teaspoon vanilla together. Pour into egg mixture into the flour mixture and mix well. Stir in the shredded zucchini. Pour batter into prepared pans. Bake in preheated oven until a tester inserted into each layer comes out clean, about 25 minutes. Allow cakes to cool in pans for 10 minutes, then invert onto a wire rack and allow to cool completely. To Make Frosting: Beat cream cheese and butter until smooth. Add the confectioner's sugar, a little at a time, and beat until smooth. Stir in 2 teaspoons vanilla. Spread between cake layers and stack to make a 3-layer cake.