My family has only ever used one cake recipe and it's vegan (I'm the only vegan in the family). It's from the Hershey's cookbook. Sorry, it's in American measurements but I googled it and found 1 cup is 225 ml. A teaspoon is 5 ml. and a tablespoon is 15 ml.
Lickety-Split Cocoa Cake
1 1/2 cups unsifted all-purpose flour
1 cup sugar
1/4 cup Hershey's cocoa
1 teaspoon baking soda
1/2 teaspoon salt
1 cup water
1/4 cup plus 2 tablespoons vegetable oil
1 tablespoon vinegar
1 teaspoon vanilla
Combine flour, sugar, cocoa, baking soda and salt in large bowl. Add water, oil, vinegar and vanilla; stir with spoon or wire whisk just until batter smooth and ingredients are well blended. Pour into greased and floured 9-inch layer pan or 8-inch square pan. Bake at 350 degrees for 35 to 40 minutes or until cake tester comes out clean. Cool in pan; frost as desired. 6-8 servings.
This is about half as much cake as a normal cake pan so just double the recipe.
For other recipes google "depression era cake". During the US great depression people found ways of doing things without dairy and eggs because of the expense.