Adjust oven rack to lower-middle position and heat oven to 300 degrees. Grease and flour 12 cup non-stick tube pan (you can also use bundt pan which is what I did). Process sugar, eggs, 7 Up, lemon zest and juice, lime zest and juice, and salt in food processor until smooth. With machine running, slowly pour in butter and process until incorporated. Transfer to large bowl. Add flour in three additions, whisking until combined.
Spread batter in prepared pan. Gently tap pan on counter. Bake until toothpick inserted in center comes out clean, 75 to 90 minutes. Cool cake in pan 10 minutes, then turn out onto wire rack set inside rimmed baking sheet to cool completely, about 2 hours.
Glaze: Whisk confectioners’ sugar, lemon juice, and lime juice in bowl until smooth. Pour glaze over cooled cake. Let glaze set 10 minutes. Serve. Cake can be wrapped in plastic and held at room temperature for 3 days.