I have this old recipe (from my Gram) caled Wacky Cake, and there is no eggs in it. The story behind the cake was, during WW2, eggs were scarce so someone came up with this idea, and the WACS (women in the army) used to make this, hense the name Wacky Cake, (I honestly dont know how true the story is. Anyhow here is the recipe
1 1/2 cups flour
1 cup sugar
3 tablespoons unsweetend baking cocoa
1 teaspoon baking soda.1/2 teasp. salt
1 teaspoon vanilla
1 teaspoon vinegar
5 tablespoons oil
1 cup cold water In a large mixing bowl mix the flour,sugar,cocoa,soda and salt. Put into 8 x 8 pan, and make 3 wells in the mix, in one well add the vanilla,in another add the vinegar, and in the 3rd add the oil. Pour the water all over, and mix well. I have made this a few times and everyone likes it. Good luck.