OK. I just downloaded the motherboard manual. It's a server board.
According to the manual (pages 1-12 and 1-13), if you are using a 64 bit CPU, you need both connected. How using only 1 cpu would affect that, I don't know. I would plug both in.
Suggestion: When you write in asking for help, give all the system details. For example, a better way to ask this question would have been,
" I have a SUPERMICRO X7DBE with 1 CPU only, Intel Xeon E5310 Clovertown 1.6GHz. In addition to the main power connector, it has both 4 and 8 pin power connectors. With one CPU, do I need to use both connectors?"