Line an 8 x 8 baking pan with parchment paper. Leave a few inches of paper hanging over the sides to act as handles to remove the fudge later.
Add the cake mix and powdered sugar to a large microwave-safe bowl. Stir just enough to blend. Add the butter and milk. Do not stir. Microwave on High for 2 minutes. If the butter is not completely softened, microwave on High for another 15 seconds. Add the white chocolate chips to the mix and immediately stir to combine.
Allow the mix to cool for 3 minutes. Stir in the red and green chocolate candies, until the candies start to melt and the mix looks marbled. Scrape into prepared pan. Use a spoon to spread into an even layer.
Refrigerate until firm, about 1 hour. Lift the chilled fudge out of the pan using the parchment handles. Cut into 1-inch squares with a sharp knife.