Pre-heat the oven to 180°C/160 fan/ gas mark 4. Grease and lightly dust with flour a 10 cup/2.4 litre bundt tin.
Place the sugar and lime zest in a mixer and blend together for a few minutes until the zest is evenly dispersed and a citrusy fragrance fills your kitchen.
Drop the butter into the mixer cube by cube, it will gradually cream together with your citrus sugar. When it’s all incorporated beat on a high speed for a few minutes until it’s very light and fluffy.
Add the eggs one at a time until they are thoroughly incorporated.
Add the banana into the creamed butter and sugar. Mix together, scraping down the sides of the mixer so it is all completely mixed in.
Whisk the flours together in a separate bowl along with the baking powder and salt and set aside.
Stir the sour cream, vanilla and rum together in a small jug.
Add the flours and sour cream mixture alternately into the rest of the cake batter in the mixer. Start with the flour, then the sour cream. The flour should be added in three additions, the sour cream in two and mix until just incorporated.
Pour the batter into the bundt tin, smoothing the surface.
Bake for around 60 minutes or until an inserted cocktail stick comes out of the cake clean. If the cake is browning a little too much on top halfway through the bake, dome a piece of foil over the top loosely to protect it.
Remove the cake from the oven, leave to settle for five minutes then loosen the top edges of the cake from the tin with a small palette knife as those are the bits that tend to stick. Turn the tin upside down onto a cooling rack and remove.
Leave the cake to cool completely on the cooling rack.