Position rack in lower third of oven. Preheat oven to 350 degrees. Coat 8 or 10 cup fluted tube pan with spray.
Combine flour, baking powder, baking soda, and salt in bowl. In another bowl, stir 1/3 cup sugar, cocoa, coffee, and water until smooth. Whisk whole egg and egg white in cup; set aside.
Beat butter in mixer bowl until creamy, 1 minute. Gradually add remaining 1 cup sugar and beat at high speed about 3 minutes. Gradually add eggs; beat 2 minutes. With mixer at low speed, add dry ingredients alternately with yogurt, beginning and ending with dry ingredients. Beat until well blended. Measure 1 1/2 cups batter and stir into cocoa mix. Spoon about 3 quarters of the white batter evenly into bottom of tube pan. Spoon on dollops of chocolate batter, then small dollops of white batter over the chocolate. Draw small knife thru batters in zigzag motion to marbleize. Be careful not to overblend.
Bake 45-50 minutes, until toothpick inserted in center of cake comes out clean. Cool in pan 10-15 minutes. Unmold cake; cool completely.