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Melt the white chocolate in a glass bowl in a microwave oven. Stir in 6 pieces of the butter until melted, then stir in 2 1/2 tablespoons of the heavy cream. Scrape the white chocolate ganache into a clean bowl and let cool.
Put one-fourth of the bittersweet chocolate in a small bowl. In a small saucepan, combine the remaining butter and heavy cream with the corn syrup and bring to a boil. Pour the cream over the chocolate and let stand for 2 minutes, then whisk until smooth. Let the ganache cool to room temperature.
Swirl the two ganaches with a knife and refrigerate until firm. Scoop scant teaspoons of the ganache onto a baking sheet and chill for 15 minutes. Roll each truffle into a ball and chill until firm.
Melt two-thirds of the remaining bittersweet chocolate in a microwave oven. Scrape the chocolate into a clean bowl and stir in the remaining chopped chocolate until smooth. Using a fork, dip the truffles into the melted chocolate to coat and set them on the baking sheet. Top with sprinkles and refrigerate until firm or for up to 1 week.