For the cake: Preheat the oven to 350 degrees F. Generously spray a 10-cup Bundt pan with nonstick baking spray with flour.
Add the butter, sugar, salt, baking powder, vanilla, oil and citrus zests to the bowl of a stand mixer fitted with the paddle attachment and beat on medium speed for 4 minutes. Stop the mixer and scrape the bowl and beater. Add the eggs, 2 at a time, beating on medium speed for 30 seconds after each addition. Scrape the bowl.
Add 1 1/2 cups cake flour and blend on low to combine. Add the cream and buttermilk and blend on low to combine. Scrape the bowl. Add the remaining 1 1/2 cups cake flour, blending on low to combine and then raise the mixer to medium speed and beat for 4 minutes. Transfer the batter to the prepared pan.
Bake the cake until a toothpick inserted near the center comes out with a few moist crumbs, 65 to 70 minutes. The cake will rise to fill the pan and will settle slightly once removed from the oven.
Meanwhile, for the syrup: While the cake bakes, juice the lemon and oranges to make 1/2 cup of citrus juice. Transfer the juice to a small saucepan and add the sugar. Bring the mixture to a simmer and swirl the pan to dissolve the sugar. Turn off the heat. Reserve the syrup at room temperature while the cake bakes.
When you've removed the cake from the oven, use a toothpick to pierce the top crumb of the cake about 30 times and then slowly pour the syrup evenly over the hot cake. Cool the cake in the pan for about 30 minutes before turning out of the pan on a wire rack to cool completely before serving.
Using a baking pan spray that contains flour is the secret to ensuring that your Bundt cake unmolds easily from the pan.
The flavor and texture of this cake intensifies and improves even more after sitting overnight.