Preheat oven to 200°C (400°F)
Pour the yogurt into a bowl.
Add sugar and vanilla sugar, lemon zest, and whisk.
Separate the egg whites and yolks. Add the yolks to the previous mixture. Reserve the whites.
Gradually stir in the olive oil.
In a separate bowl, mix together the flour, baking powder and salt. Add them to the liquid mixture.
Add the rum.
Beat the egg whites until stiff.
Take about 1/3 of the egg whites and add them to the dough to smooth it out.
Gently fold in the remaining whites until you have a smooth batter.
Pour the batter into the pan (previously greased and floured).
Bake for about 30 minutes, or until the cake is cooked.