Put sugar, vanilla sugar, and eggs in a bowl.
Whisk everything lightly and airy with an electric mixer.
Fold the oil into the airy egg mixture.
Put flour, baking powder, and salt in a new bowl and mix it together.
Take a sieve and sift the dry mixture into the bowl with the wet mixture.
Fold everything together.
Use a citrus peeler or grater to grate lemon zest into the batter. Peel the zucchini and cut it lengthwise to scrape out the “seeds” from the middle with a tablespoon.
Then coarsely grate the zucchini on the grater and fold the grated zucchini into the batter. Find a springform pan or another cake pan. I used this slightly different pan. Clip a piece of parchment paper to just cover the bottom of your pan.
Place the parchment paper at the bottom of the cake pan.
Pour the cake batter into the pan.
Put the cake in a preheated oven at 180 degrees Celsius (356 degrees Fahrenheit), regular top and bottom heat. Let the cake bake for about 30-35 minutes.
Take the finished cake out of the oven.
Let the cake cool in the pan.
Release the cake from the pan once it has cooled.