Preheat oven to 325° F. Thoroughly grease and sugar the bundt pan.
Zest the four mandarins.
Remove the peel from the zested mandarins and clean off most of the white pith. Separate the sections. Using a rimmed plate to catch the juices, cut each section into small slices with scissors. You should have about 1 ¼¼ cups of slices and juice.Try to make the mandarin pieces pretty small to avoid large wet spots in the baked cake.
In a small bowl combine the sugar and the mandarin zest. With your fingers mix the sugar and zest until well combined and the sugar has turned orange.
In a large mixing bowl beat the softened butter for two minutes. Add in half the sugar/zest mixture, beat again for two minutes then add the remaining sugar/zest mixture and beat for four minutes. Scrape the bowl occasionally.
Add the eggs one at a time, beating each until just combined.
On the lowest mixer setting beat in the cake flour, baking soda, and salt, then scrape the bowl.
Beat in the sour cream and scrape the bowl again.
With a rubber spatula, fold in the mandarin segments and the juice.
Pour the batter into the prepared bundt pan. Tap the pan on the counter to remove any air bubbles.
Bake about 1 ¼ to 1 ½ hours until a cake tester at the center of the cake comes out clean. Let cool for 15 minutes then turn out the cake on a cooling rack to cool.See the tips below for removing the cake from the pan.