There's something called Ener-G egg substitute that's vegan, that might work, but in my experience the cake won't look or taste like the cake you're used to, so be prepared. It can still be really good but it'll be a little different.

If you use silken tofu in a cake recipe, your son wouldn't have a clue it's even there -- tofu is pretty flavorless. He may not like to eat it as a separate item in a dish, but blended in it's unnoticeable. I used it in a pumpkin pie once instead of eggs and cream and no one knew the difference. But I understand if you don't want to do that.

If you have a chance, visit a bookstore or library and look at the vegan cookbooks (the vegetarian cookbooks will mostly use eggs) and their cake recipes. You should be able to find something there.

There's also lots on the web. I'm including a link below that talks about baking eggless cakes and also has some recipes. And here's a link to copy and paste into your browser, it has several recipes:

http://members.terracom.net/~dorothea/cakes.html

and I haven't tried this but it got great reviews, and if you don't want to buy soy milk you can use regular milk.

Rich Chocolate Cake

Well the name says it all. This is the richest chocolate cake around. To make it a 2 layer cake, multiply the ingredients by one half and divide into 2 seperate springform pans. If you don't have springform pans, cover the bottoms in parchment paper or it will stick.
Equipment:
springform pans, 2 good sized bowls, a wisk, saucepan

Ingredients
3/4 cup whole wheat pastry flour
1 cup all purp unbleached flour
2 teaspoons baking powder
1 teaspoon baking soda
3/4 cup good cocoa powder
1/2 teaspoon salt
1 cup plain soymilk
1/2 cup canola oil
1 1/2 cups pure maple syrup
1 teaspoon apple cider vinegar
2 teaspoons vanilla

Directions
Preheat oven to 350 F. Spray a 9 inch springform pan with non stick cooking spray.

Sift together flours and baking powder and baking soda.

In a saucepan, heat the soymilk on low-medium heat. When it is slightly bubbling, add the cocoa powder and wisk well until it is dissolved. Remove from heat.

Combine the other liquid ingredients in a bowl and whisk well. Add the cocoa mixture and combine. Add the wet ingredients to the dry.

Pour batter into prepared pan, bake at 350 F for 25 minutes until a toothpick or butter knife comes out clean. Let cool completely and frost with your favorite frosting.

Here is a link that might be useful: about eggless cakes

Thank you for your help Carol Ann, I posted this on the cooking forum also and Tammy told me about the same egg replacer. I think I have a good recipe now. This one sounds good (I know I saw it in one of the vegetarian books I got from the library) but I don't have any maple syrup on hand. Really bad weather day here so I can't get to the store. Here is the recipe I am going to use, I found it in The Passionate Vegetarian, some of the ladies on the cooking forum have used it and said it is good.
Here is the recipe:
Here is one for a 9x13:

INGREDIENTS

* 3 cups all-purpose flour
* 2 cups white sugar
* 1 teaspoon salt
* 2 teaspoons baking soda
* 2/3 cup unsweetened cocoa powder
* 1/2 cup vegetable oil
* 2 tablespoons distilled white vinegar
* 2 teaspoons vanilla extract
* 2 cups cold water

DIRECTIONS

1. Sift flour, sugar, salt, soda, and cocoa together into a 9 x 13 inch ungreased cake pan. Make three wells. Pour oil into one well, vinegar into second, and vanilla into third well. Pour cold water over all, and stir well with fork.
2. Bake at 350 degrees F (175 degrees C) for 30 to 40 minutes, or until tooth pick inserted comes out clean. Frost with your favorite icing.

I have also made it as a layer cake and a bundt cake. Just grease and flour the pan. Or grease and dust with cocoa powder. And mix the cake in a bowl as usual.