The contact form on the Southern Living website includes an option for recipes, so this is one way to submit a cake recipe to the brand. As of 2015, the physical address to send correspondence, including recipes, is Southern Living Customer Service, P.O. Box 62120, Tampa, Florida, 33662-2120.
The Southern Living group also promotes a sister website, MyRecipes.com, which features many more tasty recipes. It is possible that a recipe submitted to Southern Living will be used on this site rather than the main Southern Living site if accepted, as the sites are all part of the same brand, and by submitting a recipe, the creator hands usage rights over to the organization.