Sounds like some of the songs are in a format your burner software does not like / has problems converting. These might be mp3pro which is a propriety format ... not so common nowadays but still used. Or might be another format your burner program is having problems recognising & converting. For them to show O KB is ominous.

Have you checked for updates for your Cyberlinks Power2go? Play those songs from the list you could not burn, verify they play properly from beginning to end (those that show the 0 KB after adding to burner).
What audio file extensions do the songs have that are on the list you cannot burn?

Although you won't be able to play in most stereo systems, you could use CD-RW disks whilst you try to solve this problem to save you CD-R disks. (Some DVD players & some of the newer CD players will play CD-RW disks, but CD-RW disks for audio should not be a permanent disk medium to use. Only use it for testing. Your computer player should be able to play CD-RW audio disks.)