Prepare cake as directed on package; cool.
In a 3-quart saucepan over medium heat, melt butter; add cocoa and sugar. Stir until smooth.
Add apricot preserves and vanilla. Stir until smooth and glossy. Remove saucepan from heat.
Crumble cake into mixture in saucepan. Mix until well blended and moist. Roll into 1-1/2-inch balls.
In a small, heavy saucepan over low heat, melt semi-sweet chocolate, stirring until smooth.
Dip truffles into melted chocolate, one by one, completely coating each with chocolate. Place on waxed paper until set, at least 1 hour.