Move oven rack to lowest position. Preheat oven to 350 degrees F.
Combine the water coffee liqueur, and instant coffee in a mixing bowl. Stir until coffee is dissolved.
Add cake mix and cocoa powder using a electric mixer on low for 30 seconds, then beat on medium for 1 minute. Pour into an ungreased 10 by 4 inch tube pan. Bake in preheated oven for 37 to 47 minutes or until top it a dark golden brown, cracked and not sticky.
Remove from oven and turn pan upside down onto a bottle until completely cooled. Run a knife around edges of pan and remove cake from pan.
Icing: stir together all ingredients in a bowl until smooth. Pour over the top of the cake and let it run down the sides. Let icing set for 1 hour.