Greas a normal loaf pan and preheat oven at 350 degrees F.
Combine in a large bowl sugar, eggs, sour cream, lemon zest, juice, vanilla, and oil. Stir until completely blended and smooth.
In another dish, sift salt, baking powder, and flour.
Add the dry ingredients gradually to the wet until well blended; then put aside.
For the cream cheese swirl, gently stir the cream cheese and powdered sugar in a small bowl until smooth.
Spoon half the batter to the ready pan; top with half the cream cheese mixture; then, whirl together with a knife.
Top with the remainder of the batter then spoon the remaining cream cheese mixture. To provide a marbled appearance, gently swirl together.
Bake bread for 65 to 70 minutes; cover with foil for the final 20 to 30 minutes to stop the top from browning.
Before cutting, let the bread completely cool so the cream cheese sets.
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