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 for 45 minutes or until a wooden pick inserted in center comes out clean. Cool the cake on a wire rack.