Preheat the oven to 350 degrees F.
Grease a 10-12 cup Bundt cake pan. Set aside.
In a stand mixer fitted with the paddle attachment, add the cake mix, pudding mix, cake flour, and sugar. Mix on low for about 20 to 30 seconds.
Increase the speed to medium and mix for 2 minutes, scraping the bowl and blade as needed.
While the batter is mixing, place the strawberry jam/puree in a separate medium bowl. Add a few drops of red coloring if desired. Set aside.
After the batter has mixed for 2 minutes, pour about a third of the batter into the bowl with the jam/strawberries and blend together.
Pour about ⅓ of the white cake batter into the bottom of the greased Bundt pan. Pour the strawberry jam batter over the white batter, spreading evenly.
Pour the remaining white batter over the strawberry mixture. Smooth the top. If preferred, you can use the handle of a spoon to swirl, or you can leave the layers as is.
Bake in the preheated oven for 35 to 40 minutes. Begin testing for doneness with a toothpick at 35 minutes, especially if your oven runs on the hotter side. Bake until the toothpick comes out with just a few crumbs attached.
Remove the pan from the oven and set it on a heat-proof surface; allow to cool for 20 minutes.
Invert the warm cake onto a cake stand/platter and allow it to completely cool if frosting.
The cake may be served warm if just a dusting of powdered sugar is used.
Any leftovers may be kept in an air-tight container at room temperature or refrigerated for 4 days. The cake may be frozen, well-wrapped without frosting for up to 3 months. Thaw then frost is previously frozen.