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Put the sliced and halved strawberries for the filling and decoration into a small bowl and pour over the Pimm's. Leave to soak in for at least one hour or overnight. Heat oven to 190C /170C fan/gas 5. Line 3 x 20cm sandwich tins with baking parchment and grease with butter.
Cut the whole cucumber in half lengthways and using a teaspoon scrape out and discard the seeds. Roughly chop the rest of the cucumber and puree in a blender with the lemon juice.
In a large bowl and using electric beaters whisk up the softened butter with the sugar until pale and light. Continue whisking as you add the eggs, one at a time, whisking in between additions. Once all the eggs have been added pour in the cucumber purée, lemon zest and vanilla extract. Don’t worry if the mixture splits - it will come back together when you add the flour.
Fold in the flour and baking powder and whisk once again briefly until there are no lumps of flour remaining then divide the mixture between the three tins. Bake in the oven for 30-35mins or until a skewer pushed into the middle of the cakes comes out clean. Take the cakes out of the oven and leave to cool in their tins for five minutes then turn out onto wire racks to cool completely.
While the cakes are cooking and cooling make the buttercreams. To make the strawberry buttercream, mash the strawberries in a small bowl with a fork until mushy. In a larger bowl whisk up the butter and half the icing sugar until smooth, then whisk in the mashed strawberries followed by the remaining icing sugar. Whisk until smooth and pale pink and place in the fridge until needed. Repeat the process with the lemon buttercream.
Once the cakes are completely cold, put one of the cakes onto a cake turntable and add about one third of the lemon buttercream, spread over the surface evenly then top with half of the soaked strawberry slices. Next, spread one third of the strawberry buttercream onto another of the cakes and top with the remaining strawberry slices. Carefully stack the two filled layers with the final cake on top.
Transfer the remaining buttercreams to disposable piping bags and snip off the ends. Pipe the strawberry buttercream in rings around the outside of the cake, starting at the base. Once you reach three quarters of the way up, switch to the lemon buttercream and continue piping onto the top of the cake. Smooth over the top using a palette knife then smooth the sides with either a large palette knife or, better still a pastry scraper. Use long sweeping movements and gently turn the cake turntable so that you get a smooth finish but a subtle gradient effect where the two colours meet. Scrape any excess icing into a bowl.
To finish, top with the remaining soaked strawberry halves and the slices of cucumber.