Preheat oven to 350°F. Line a 9x5-inch loaf pan with parchment paper and set aside.
In a small bowl, blend the white granulated sugar and lemon zest together by rubbing it together in between your fingers, set aside.
In a large bowl using a hand held mixer or a stand mixer with the paddle attachment, cream the butter and sugar with lemon zest until light and fluffy.
Add eggs one at a time, mixing well after each addition.
Mix in the sour cream, lemon juice, vanilla bean paste, and lemon syrup until combined on low speed.
In a separate bowl, whisk together the flour, salt, baking powder, and baking soda.
Add the dry ingredients to the wet ingredients and mix just until combined.
Spread the batter into the prepared loaf pan and smooth the top.
Bake for 50–60 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 15 minutes, then transfer to a wire rack to cool completely.