Preheat oven to 350 degrees F (175 degrees C).
Grease 24 muffin cups or line with paper liners.
Mix together vanilla cake mix, 1 cup water, vegetable oil, and eggs in a mixing bowl with an electric mixer on low speed until cake mix is moist. Raise mixer speed to medium and beat until batter is smooth, 2 minutes.
Spoon batter into prepared muffin cups, filling them about 2/3 full.
Bake in the preheated oven until cupcakes are very lightly browned and a toothpick inserted into the center of a cupcake comes out clean, 18 to 23 minutes.
Cool cupcakes in the pans for 5 minutes; transfer cupcakes to cooling rack to finish cooling.
Place raspberries, 1 tablespoon water, and white sugar in a blender and pulse several times to chop raspberries; blend until pureed, about 30 seconds.
Whisk cornstarch with 1/4 cup water until thoroughly combined; pour mixture into the raspberry mixture in the blender and blend again until smooth.
Pour raspberry mixture into a saucepan and simmer over low heat until thickened, about 5 minutes. Let the raspberry filling cool.
Cut a core out of each cupcake about 1 1/2 inches long and 1 inch in diameter.
Spoon about 2 teaspoons raspberry filling into each cupcake.
Place white chocolate chips in a microwave-safe bowl and heat in 30-second intervals until chips begin to melt, about 1 minute. Stir and repeat, heating chips about 10 seconds at a time, until thoroughly melted. Stir until chocolate is smooth and no more lumps remain.
Beat butter with an electric mixer on medium speed in a mixing bowl until fluffy. Beat in half the confectioners’ sugar, melted white chocolate chips, and milk until mixture is smooth and creamy.
Slowly beat in remaining confectioners’ sugar until smooth; if frosting is too stiff, beat in more milk, 1 teaspoon at a time.
Spread or pipe the white chocolate frosting over the cupcakes to cover the raspberry filling; drizzle or pipe any remaining raspberry filling over cupcakes.
If using a piping bag and decorative tip to ice the cupcakes, make sure that the white chocolate is completely melted and there are no small chunks.
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