Preheat the oven to 180ºC, fan 160ºC, gas 4. Grease and line 3 x 20cm round cake tins. Put the raspberries in a food processor and whizz until smooth. Pass through a sieve until you have a smooth sauce. Set aside.
Place the butter in a large bowl and add the sugar. Beat with an electric hand whisk for about 5 minutes until the mixture is pale and fluffy. Slowly add the eggs, beating all the time, then fold in the flour and baking powder.
Divide the mixture evenly between three bowls. In a jug, mix the cocoa powder with 3 tablespoons of boiling water then fold this into the mixture in the first bowl.
Add 3 tablespoons of the puréed raspberries to the second bowl, then add the vanilla extract to the third bowl. Stir both to combine. Spoon the mixture from each bowl into a prepared tin and bake for 15-20 minutes until lightly golden and a skewer inserted into the centre comes out clean. Turn out onto a wire rack and let cool completely.
Meanwhile, make the icing. Place the softened butter in a large bowl and beat in the soft cheese, yogurt, icing sugar and the remaining raspberry purée. The mixture should be smooth and thickened.
Put the chocolate sponge onto a cake stand and spread over 3 tablespoons of icing. Top with the raspberry sponge and repeat with another 3 tablespoons of icing. Finish with the vanilla sponge, then spread the remaining icing over the top and side of the cakes. Decorate with the fresh strawberries.