Allergens on Product Variations

I’m working on a site which sells custom cakes. Customers choose their cake (5 flavors), filling (5 flavors), and frosting (5 flavors) in 4 different sizes. Instead of creating 500 separate products, I created 5 products based on cake flavor, each with 100 variations. Some fillings and frostings add additional allergens. As an example, a Nutella frosting adds hazelnuts and soy in addition to the eggs, dairy, and wheat already present in the cake itself.

What’s the best way to proceed?