Preheat oven to 180 C / Gas 4. Grease and lightly flour four 23cm cake tins.
Whisk flour, 1 teaspoon salt, baking powder and bicarbonate of soda together in a bowl.
Beat 350g butter in a stand mixer fitted with the paddle attachment until creamy, about 1 minute. Beat in caster sugar on high speed, scraping the bowl with a spatula as needed, until fully incorporated, about 5 minutes. Reduce speed to medium-high; beat in eggs one at a time. Beat in 1 tablespoon vanilla extract.
Mix flour mixture into the creamed butter mixture in 3 additions, alternating with buttermilk, until cake mixture is smooth and slightly thick.
Divide cake mixture evenly among 4 bowls. Tint each portion of cake mixture with green, blue, purple or pink food colouring; stir until smooth. Pour cake mixture into the prepared cake tins.
Bake in the preheated oven until a skewer inserted into the centre comes out clean, about 25 minutes. Set cake tins on wire racks and let cakes cool completely, about 25 minutes.
Beat 350g butter and cream cheese in a stand mixer fitted with a clean paddle attachment until creamy, about 2 minutes. Add icing sugar, cream and 1 tablespoon vanilla extract; beat on low speed for 30 to 60 seconds.
Increase speed to high and beat icing until fluffy, about 3 minutes. Scrape down the sides of the bowl as needed. Beat in a pinch of salt.
Cut a 10cm circle out of the centre of 2 cake layers using a round cutter.
Place one of the intact cake layers on a cake stand or serving plate. Spread icing over the top of this cake. Position one of the cake rings on top. Spread buttercream over the top and inside the circle. Repeat with second cake ring. Fill the hole with sweets and sprinkles. Place remaining cake layer on top. Ice the top and sides of the entire cake.
Tint any remaining icing with pink food colouring and pipe decoratively over the cake. Cut cake into slices; spoon any sweets and sprinkles that spill out over the slices.
Add more icing sugar if icing is too thin or another tablespoon of cream if icing is too thick. Add an extra pinch of salt if icing is too sweet.