Preheat oven to 325 degrees F. Liberally (and I mean VERY liberally) grease a 10 or 12 cup Bundt pan with shortening and flour. Tap out the excess flour. Set aside.
In the bowl of a stand mixer, cream together the butter and sugar until pale yellow and fluffy, about 3 minutes. Add in the eggs, one at a time, beating well after each addition. Add in the lemon juice, lime juice, vanilla, and zests of both lemon and lime and beat well. Alternate adding in the flour and lemon lime soda, beating well after each addition. Lastly, stir in the drained cherries.
Spread the mixture into the Bundt pan and smooth out the top. Bake for approximately 60-70 minutes or until a toothpick inserted near the center comes out clean or with moist, not wet, crumbs. Cool for about 20 minutes in the pan, then carefully invert it to a wire rack to finish cooling.
Once cooled, poke holes all over the cake with a skewer or toothpick. Slowly pour the maraschino cherry juice over the poked holes in the cake and let set about 15 minutes. Meanwhile, prepare your glaze by whisking all the glaze ingredients together in a medium bowl. Drizzle the glaze evenly over the cake. Allow glaze to set, about 15-20 minutes, before serving.