Preheat the oven to 325 degrees F.
Using the extra butter, grease a 10-inch fluted tube pan, then using the extra flour, lightly dust the greased pan.
In a large bowl, add 1 1/2 cups of the remaining butter and 2 3/4 cups of the sugar and, using an electric handheld mixer, beat until light and fluffy, about 5-7 minutes.
Add the eggs, 1 at a time, to the butter mixture and beat well after each addition.
Add the vanilla to the butter mixture and beat until combined.
In a separate bowl, add 3 cups of the remaining cake flour and the salt and whisk to combine.
Add 1/3 of the flour mixture to the butter mixture and beat well to combine.
Add 1/3 cup of the ginger beer to the butter mixture and beat well to combine.
Add 1/2 of the remaining flour mixture to the butter mixture and beat well to combine.
Add 1/3 cup of the remaining ginger beer to the butter mixture and beat well to combine.
Add the remaining flour mixture to the butter mixture and beat to combine.
Add 1/3 cup of the remaining ginger beer to the butter mixture and beat to combine. Don't worry if the batter looks curdled.
Add the raspberries to the batter and gently fold to combine.
Pour the batter into the prepared pan.
Bake until a toothpick inserted near the center comes out clean, about 1 hour 10 minutes-1 hour 20 minutes.
While the cake bakes, in a small saucepan, add the remaining 1/2 cup of the ginger beer, the remaining sugar, and 1/4 cup of the lime juice and stir to combine.
Bring the syrup mixture to a boil.
Reduce the heat to low and simmer the syrup mixture until it thickens slightly, about 10 minutes.
Cool the syrup slightly.
Transfer the cake to a wire rack, then while the cake is still in the pan, using a fork or a wooden skewer, poke holes in the cake.
Slowly spoon the syrup over the cake.
Allow the cake to cool in the pan for 15 minutes.
Transfer the cake from the pan to a wire rack to cool completely.
In a small bowl, add the confectioners' sugar and 2 tablespoons of the lime juice and whisk to combine. If the glaze is too thick, add the extra lime juice, a little at a time, until the glaze reaches a consistency that can be drizzled.
Pour the glaze over the cake and let stand until it is set.
Serve.