Preheat oven 350 degrees.
Grease and flour cake pan.
Ina medium bowl, combine flour, cocoa, baking soda and baking powder, set aside.
In a large bowl with mixer at high speed, beat eggs, sugar and vanilla, scraping bowl occasionally, for 3 minutes or until smooth and creamy.
Reduce speed to low, beat in mayonnaise until blended.
Add flour mixture in 4 additions alternately with water, beginning and ending with flour.
Pour into prepared pans.
Bake 30 to 35 minutes or until cake springs back when touched lightly.
Cool in pans on cooling racks for 10 minutes.
Remove from pans, cool completely on rack.
Refrigerate before frosting.