Preheat oven to 375° F. In a medium bowl, stir together flour, baking powder, and salt until combined. Set aside.
Using a stand or hand mixer with a large bowl, beat in eggs one at a time until incorporated. Beat on low until thickened and pale yellow, about 3 minutes.
Add sugar and beat on medium until light and fluffy, 3-5 minutes.
Beat in lemon and lime juices, zests and vanilla until combined.
Reduce speed to low and carefully add flour mixture until combined. Add milk, 7-Up, and butter and beat until combined.
Grease a bundt pan until well coated with butter or oil and lightly flour surface. Pour in batter and bake 30-35 minutes, or until toothpick inserted in center comes out clean with just a few moist crumbs.
Cool on a wire rack 5 minutes then flip and release cake. Top with lemon glaze and sugar crumble.
Lemon Glaze and Sugar Crumble
Meanwhile: Whisk together powdered sugar and lemon juice (use more or less for desired thickness). Drizzle over slightly warm cake.
Stir together sugar with zests and sprinkle on top. Optional: Top with lemon slices to enhance presentation.
Use freshly squeezed lemon juice for best flavor.
For stronger lemon flavor you could add additional lemon extract or extra lemon zest.
As with most cakes, sift flour before adding to remove clumps. This will eliminate chunks of flour and help the lemon cake rise better.
If you don't have a stand or hand mixer, you can whisk by hand. It will take longer and be sure to stir well to evenly mix.
Since bundt cake pans have an intricate design, grease the pan well, then lightly sprinkle with flour to ensure the cake doesn't stick and removes easily after baking. A paper towel or pastry brush works best to apply oil.
Add eggs one at a time beating well after each addition so they incorporate evenly into the batter.
If you don't have a bundt pan, you could substitute a pound cake or similar cake pan. The baking time should be similar.
Let the cake cool slightly before removing from the pan. It will shink a bit and release from the sides.
Add the glaze while the cake is still warm so it soaks into the bake. Then let cool completely to room temperature so the glaze can thicken.
After baking, a toothpick should come out mostly clean, with just a bit of cake sticking to it. If the toothpick still has wet batter it's undercooked and should be baked an extra 1 to 3 minutes. If it comes out completely dry, it may be overcooked.