PREPARE LAYERS. Combine coffee, sugar and water to make black coffee. Combine the black coffee, sugar and rum in a bowl. Dip the graham cracker crumbs in the coffee and rum mixture. Lay the soaked graham crackers on a dish. Reserve for use later.
DO COFFEE CREAM FILLING. In a bowl, whisk together the cream cheese and powdered sugar until light and fluffy. Add 2 tablespoons rum.
WHISK the all-purpose cream in another bowl until it doubles in volume.
FOLD the whipped cream into the cheese mixture, making sure both are blended thoroughly. Divide into three equal parts.
Lay 6 pieces of Grahams. Pour 1/3 of coffee cream. Spread evenly. Do another layer alternating crackers and cream. Chill until cream is set. Sift with cocoa powder on top. Serve.