If you're making the mermaid tails, melt the white chocolate in a heatproof bowl in 20-second bursts in the microwave, stirring after each turn. Pour into the tail moulds and small shells, and put on a small tray flat in the freezer for 15-20 mins until set. You can repeat this for four tails if you only have one mould.
Once set, remove from the mould, mix the lustre with ¼ tsp of water and paint it onto the mermaid tails (see tip, below). Put back on a plate or tray in the freezer until needed.
Heat the oven to 180C/160C fan/gas 4. Butter and line the base of three 18cm sandwich cake tins with baking parchment. Using a stand mixer or electric hand whisk, beat together the butter, sugar, eggs, vanilla, baking powder and flour until you have a fluffy mix.
Divide the mixture evenly between three bowls and mix a few drops of colouring into each bowl until fully combined, making each bowl a different shade of purple, getting lighter. Pour each coloured sponge mix into separate tins and smooth over the tops. Bake for 25-30 mins until a skewer inserted into the middle comes out clean. After 10 mins, remove the cakes from their tins and transfer to a cooling rack, top-side facing down, and leave to cool. Don’t worry if the outside doesn’t look purple, the inside will!
While the cake is cooling, make the icing. Beat together the icing sugar and butter until pale and fluffy, mixing in 1 tbsp warm water to loosen the mixture if necessary. Set half of the icing aside in a bowl. Divide the other half of the icing between three bowls and colour each a different shade of blue, a dark, medium and light. Stack the sponges, spreading most of the white icing over each one using a palette knife, then use the palette knife to roughly coat the outside of the cakes with the remaining white icing to create a crumb coat. Chill for 30 mins.
Put each of the blue icing shades in separate piping bags and cut a large 2cm hole at the bottom. Starting with the dark shade at the bottom of the cake, pipe an even ring onto the whole cake, two-three times around. Continue working your way up the cake with the icing getting lighter as you reach the top of the cake. Using a small palette knife, work your way around the join in between each row, gently pushing to join each line together. Save some icing in the piping bags to decorate the top. Smooth over the cake with a large palette knife or cake scraper to create a smooth ombre icing, keeping the excess to decorate the top.
You can either mix all the leftover icing together and put in a clean piping bag with a star nozzle to get a multicoloured effect, or pipe individual shades on the top. Add a few dots around the top of the cake in the varying blue colours to look like waves (using some of the white to look like the top of a crashing wave), and dot around the pearls, sprinkles, shells and mermaid tails, pushing them into the icing on the side of the cake, and on top to finish.