In a food processor, add the strawberries. Puree until smooth. Run the mixture through a sieve, discarding the strawberry pulp. Measure out 1/4 cup of strawberry puree and mix it with 1/2 cup buttermilk. If you want it to be a very pink hue, add 2-3 drops of food coloring into the buttermilk mixture and stir until combined. Set aside.
Preheat oven to 350 degrees. Generously butter a 9-by-5-inch loaf pan; set aside. Whisk together the cake flour, baking powder, and salt; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat the butter and sugar until light and fluffy, about 5 minutes. Add eggs, one at a time, beating until combined after each addition and scraping down the sides of the bowl as needed. Mix in vanilla. Add flour mixture in 2 batches, alternating with the strawberry/buttermilk and beginning and ending with the flour. Set aside 1/3 of the batter (about 1 cup).
In a bowl, mix cocoa and 1/4 cup plus 2 tablespoons boiling water with a rubber spatula until smooth. Add the cocoa mixture to the reserved cake batter; stir until well combined.
Spoon batters into the prepared pan in 2 layers, alternating spoonfuls of strawberry and chocolate to simulate a checkerboard. To create marbling, run a table knife (or wooden skewer) through the batters in a swirling motion.
Bake, rotating the pan halfway through, until a cake tester comes out clean, 40 to 45 minutes. Transfer pan to a rack to cool 10 minutes. Turn out cake from pan and cool completely on the rack. Cake can be kept in an airtight container at room temperature up to 3 days.