Grease and flour three 8x1-1/2-inch round baking pans. In a medium bowl, mix flour, sugar, cinnamon, baking soda, salt, and allspice.
In a large bowl, beat eggs with an electric mixer on medium to high speed until light. Add cooking oil in a stream while beating on medium speed. Beat in flour mixture until batter is smooth.
By hand, stir in carrots. Pour into prepared pans. Bake in a 350 degree F oven for 20 to 25 minutes or until wooden toothpick inserted in centers comes out clean. Cool for 10 minutes. Remove from pans; cool on wire racks.
To assemble, set 1 cake layer on serving plate. Spread half the apricot preserves over it. Top with second layer. Spread with remaining preserves. Place third layer on top. Spread side and top with Cream Cheese Frosting. Decorate as desired. Store, covered, in refrigerator. Makes 1 cake (16 to 20 servings).
In a large bowl, beat cream cheese, butter, and vanilla with an electric mixer on medium speed until light and fluffy. Gradually beat in enough powdered sugar to make a frosting of spreading consistency.