Preheat the oven to 170°C (150°C for fan assisted ovens)/Gas Mark 3. Grease and flour a 2.5-litre bundt cake tin.
Make up the cake mix as directed on the box using the oil, water and eggs, then fold through the chocolate chips. Pour the mixture into the bundt tin in an even layer.
Make the filling. In a small bowl, beat the soft cheese until smooth, then whisk in the granulated sugar, flour and egg. Spoon over the cake mixture. Gently run a knife through the mixture in a zigzag pattern. Do not mix too thoroughly.
Bake in the oven for 45-55 minutes or until a skewer inserted into the centre of the cake comes out clean. Cool in the tin for 10 minutes, then turn the cake out onto a wire rack to cool completely; about 1 hour.
Make the topping. In a small bowl, beat the soft cheese until smooth. Gradually beat in the icing sugar until you have a smooth, spoonable icing (adding a few drops of warm water, if needed). Spoon over the cake and let it partially run down the sides.
Spoon the chocolate fudge icing into a disposable piping bag and cut a small hole in the end. Pipe the icing over the top of the cake, then slice to serve.