In a medium bowl, stir together the cocoa powder and the 3/4 cup sugar. Gradually whisk in coffee until mixture is dissolved. Cool to room temperature.
Meanwhile, grease and lightly flour three 9x1-1/2-inch round baking pans. Set aside. Sift together cake flour, baking soda, and salt; set aside.
In a very large bowl, beat butter with electric mixer for 30 seconds. Add 1 cup sugar and vanilla; beat well.
Whisk or stir the sour cream into the cooled cocoa mixture. Add flour mixture alternately with cocoa mixture to the creamed mixture, beating after each addition until just combined.
Using clean beaters, in a large bowl, beat egg whites on medium to high speed about 1 minute or until soft peaks form (tips curl). Gradually add 1 cup sugar and beat on high speed until stiff peaks form (tips stand straight). Gently fold about one-third of the egg white mixture into creamed mixture to lighten. Fold in remaining egg white mixture.
Divide mixture among the three prepared pans. Bake in a 350 degree F oven for 25 to 30 minutes or until a toothpick inserted near centers comes out clean. Cool cake layers in pans on wire racks for 10 minutes. Remove the cake layers from pans and cool completely on wire racks.
Frosting: In a heavy saucepan, melt 18 ounces chopped white chocolate baking squares or bars over low heat. Cool until slightly warm. In a large bowl, beat one softened 3-ounce package cream cheese with an electric mixer until smooth. Cut 1-1/2 cups butter into pieces. Add to cream cheese; beat until fluffy. Gradually add cooled chocolate, beating until well blended.
Frost. Cover and refrigerate. Allow to stand at room temperature for 30 minutes before serving.