Preheat the oven to 350 degrees F. Butter an 8x8 inch baking pan.Combine the flour, baking soda, baking powder and salt in a bowl and set aside.In another bowl, cream the butter and sugar until pale and fluffy. Add the eggs, vanilla extract, lemon and lime juice and zests, and beat until combined. Stir in the grated zucchini and lemon squash.Add the buttermilk and flour mixture to the wet mixture, alternating in thirds and stir lightly after each addition. Do not over-stir or the cake will be dense. Stir just until combined, a few small lumps are okay.
Pour the batter into the greased baking pan and bake for 30-35 minutes or until a toothpick inserted into the center of the cake comes out clean. Let the cake cool completely.
While the cake is baking make the frosting: Combine all the ingredients, except for the powdered sugar, in a mixing bowl and beat until combined. Add the powdered sugar gradually, beating until combined.Frost the cooled cake and cut into squares.
These can also be made as cupcakes: Preheat the oven to 400 degrees F and bake the cupcakes for 16-19 minutes.