Prepare the red velvet cake according to package instructions, substituting melted butter for the oil. Pour into a 9-by-13-inch cake pan or baking dish and bake according to the package instructions. Let cool completely, then cut into bite-sized chunks (reserve crumbs).
Gently fold together the whipped topping with the frosting in a bowl. Spoon a dollop into a parfait glass, then sprinkle with candied pecans and walnuts. Top with a few pieces of the cake. Continue layering the frosting mixture, nuts and cake, finishing with a garnish of cake crumbs (tear up additional cake cubes if necessary). Repeat with remaining parfait glasses and serve immediately.