Use a mixer to beat the cream cheese, butter, and sugar together for about 5 minutes. Add the eggs individually, mixing until each is just combined.
Combine flour, baking powder, salt, dry ingredients, milk, and lemon and lime zest in a bowl. Pour into prepared pan and bake for 50-60 minutes.
Create a glaze by mixing powdered sugar, lemon juice, lime juice, and water. Place cake in pan, poke holes, pour glaze, cool, serve, and store in airtight container.