Make the dipping liquid by mixing rum, water, coffee and caster sugar. Pour into a wide bowl and set aside.
Beat mascarpone and sugar in a bowl until soft and creamy. Keep aside.
For the sabayon, mix together egg yolks, sugar and rum in a large mixing bowl. Place the bowl on a pan of barely simmering water to make a double boiler. The bowl should not touch the water. If it does, the eggs will scramble.
Using a hand mixer or whisk, beat the mixture at a high speed till it doubles in amount and becomes a thick pale yellow sauce. This will take about 5 minutes. Take the bowl off the heat and let it cool.
In a small mixing bowl, whip the cream for about 2 minutes or until soft peaks form and keep it aside.
Fold the mascarpone mixture into the cooled sabayon. Then fold the whipped cream into it gently and quickly.
Now whip the egg whites until they form stiff peaks. For this, first ensure that the beater and the bowl are clean and dry. Add the egg whites and beat until frothy. Gradually add the sugar as the mixer continues to run. Once the mixture forms stiff peaks, fold this too into the above mixture. The custard is ready.
Cut the cake into slices that would fit into a large serving dish. Dip the cakes slices in the dipping liquid and line the dish with these. Spread a thick layer of the prepared custard over the cake. Cover with another soaked layer of cake, followed by another layer of custard.
Refrigerate for anywhere between 2 to 24 hours. Just before serving, sprinkle cocoa powder over the tiramisu with a sieve.