Combine eggs, oil, sugar and vanilla; mix well. Combine dry ingredients; add to oil mixture, mixing well. Stir in the grated zucchini.
Pour batter into a greased and floured 10 inch Bundt pan. Bake at 350 degrees for 50-60 minutes. Allow to cool 20 minutes before removing from pan.
Icing: Beat together softened cream cheese, butter and vanilla. Slowly add confectioners' sugar and beat until smooth. Ice cooled cake.