[Alneyan]

You mean a Colonial Community or-that-other-facility-in-the-same-line-but-
whose-name-I-forgot?

If so, your increases production does not come from the planetary bonus, but from the production of the facility itself. So, take that Cultural Centre with X15 to planetary mineral production (figure pulled out of my hat), and build a mineral facility producing 200 minerals.

You will now have 15X200=3,000 minerals because of the bonus granted to you by the Cultural Centre, plus all the other bonuses, including happiness, mineral values higher than 100%, your mining racial aptitude, and the like. So, a facility producing a mere 200 minerals on your homeworld will end up giving you a good 4,000 minerals or more, and you will be swimming in money.

On an aside, system-wide facilities do not affect the output displayed in your colonies, but does affect total production (in the budget, research and score screens), so you may experience a gap here.