For the lemon cake, preheat the oven to 175 °C. Grease a loaf pan (or small cake pan) with butter and dust with flour. Mix the sugar and vanilla sugar with the eggs, lemon zest and lemon juice with a hand mixer until the mixture is nice and creamy and bubbles. Then slowly add the melted and cooled butter. Now mix in the sour cream. Finally, sprinkle in the flour along with the baking powder and salt and mix until you have a smooth, rather runny dough.
Pour the dough into the prepared pan and bake in the oven for about 50-60 minutes. The cake is ready when there is no more dough stuck on a knitting needle. Now remove the cake from the oven and let it cool in the pan for about 15 minutes. Meanwhile, prepare the syrup. Dissolve the sugar in the lemon juice over low heat and then simmer for another 3 minutes. Now remove the lemon cake from the mold and spread the syrup on the cake with a brush. And enjoy!
If desired, decorate the lemon cake with (lemony) icing or simply sifted powdered sugar.