That particular carrot cake recipe needs to be multiplied 5 times for your pan sizes. (assuming that each of your tiers are two layers.) You can always slice them thinner and make more layers) but for cake stability I use two layers with one layer of filling in between.
Assuming you have a Kitchen Aid small mixer you can probably fit the recipe times 2. Which means you will have to do it twice at 2 times and once as is.
Here are the total amounts of the ingredients you will need to make your first wedding cake.
You can use this as a guide when multiplying other recipes.
15 cups of flour
15 cups of sugar
5 t salt
5 Tablespoons of baking soda
5 Tablespoons of Cinnamon
7 1/2 cups of oil
20 eggs
5 Tablespoons of vanilla
7 1/2 cups of walnuts chopped
7 1/2 cups of shredded or flaked coconut
6 1/3 cups of pureed carrots
3 3/4 cups of pineapple
Cream Cheese Filling
2 1/2 lbs. of cream cheese
1 lb. of butter
15 cups of confectioners sugar (or to taste) You can use less.
juice of 2 lemons
3 Tablespoons of vanilla
This will help you in the future when making your cakes. Batter amounts per pan.
6x2 2 to 2 1/2 cups batter
8x2 same as 6 inch
10x2 4 1/2 to 6 cups
14x2 10 to 12 cups
Amount of batter you use depends on the type of batter and how much it rises. You will have to play around a little with this.
I hope this helps. And please post a picture of your first wedding cake. We would love to see it and hear about it. post it here or enter the ongoing cake decorating contest. Thanks :)