Preheat the oven to 350 degrees F (175 degrees C). Grease and flour three 9-inch round cake pans.

Mix together cake mix, milk, instant vanilla pudding, 3 whole eggs, and oil in a large bowl. Pour batter into the prepared pans.

Bake in the preheated oven until a toothpick inserted into the center of cakes comes out clean, about 25 minutes. Set aside cakes on wire racks to cool completely.

Combine sugar, butter, lemon juice, 6 egg yolks, flour, and lemon zest in the top half of a double boiler. Cook, stirring constantly, over medium heat until mixture is thick enough to spread. Remove from heat and allow lemon curd to cool completely.

Run a knife around the edges of the cake pans. Invert cakes; spread cooled lemon curd between cake layers.