Preheat oven to 325 degrees F. Liberally (and I mean it!) grease and flour a bundt pan. If you think you've greased it well, grease it again. Seriously. Set aside.
In the bowl of a stand mixer, cream together the butter and sugar until light and fluffy, about 2 minutes. Add the eggs in, one at a time, beating well after each addition. Beat in the lemon and lime juice, lemon and lime zests, and vanilla extract to combine. Then, alternating with 7-Up and flour, add each gradually until a thick and smooth batter comes together.
Pour the batter into the prepared (and very well greased and floured!) bundt pan and bake for approx. 60-70 minutes or until a toothpick inserted near the center comes out mostly clean. Leave in pan for about 20 minutes before carefully inverting to a wire rack to cool completely.
To make glaze, in a medium bowl, whisk together the glaze ingredients. Drizzle on top of the cake and allow glaze to set before cutting into slices.