Place granulated sugar and butter in a large bowl; beat with a mixer at medium speed until well-blended (about 5 minutes).
Add egg whites, 1 at a time, beating well after each addition. Beat in sour cream and vanilla. Lightly spoon flour into dry measuring cups; level with a knife.
Combine flour, baking powder, baking soda, and salt, stirring well with a whisk. Gradually add flour mixture to sugar mixture; beat well.
Spread half of batter into an 8-inch square baking pan coated with cooking spray.
Sprinkle half of walnut streusel over batter.
Spread remaining batter over streusel. Top with remaining streusel.
Bake at 350 for 45 minutes or until a wooden pick inserted in center comes out clean. Cool the cake on a wire rack.