Prepare the cake mix according to the package directions for a 9-by-13-inch cake or two 9-inch cakes. Allow to cool slightly in the pan, then remove to a rack, cover with a dish towel and let cool completely.
Break off sections of the cake and crumble in a large bowl. When finished, you should have a bunch of very fine cake crumbs. Using a rubber spatula, work the frosting into the cake until it is no longer visible. (Even if you use white frosting with red velvet cake, the white will eventually blend in entirely.)
Next, roll the mixture into 1 1/2-inch balls (a small ice cream scoop helps with this) and set on a parchment-lined baking sheet. This is important: Pop 'em in the freezer, uncovered, for at least an hour. The cake balls need to be very firm before coating them.
When the cake balls are nice and firm, place the white chocolate in a heatproof bowl set over a pan of simmering water. (Don't let the bowl touch the water.) Stir occasionally until the chocolate is melted and smooth. Remove the bowl from the pan. Add the cake balls one at a time to the melted white chocolate and gently roll to coat. Using a fork, lift out the cake balls, then tap the fork against the side of the bowl to remove the excess chocolate. With a toothpick, push the ball off of the fork and back onto the parchment-lined baking sheet. Let set at room temperature, 10 to 15 minutes. Decorate with gel icing to look like eyeballs.