This is a question where the terminology is important.  If by “sponsor” you mean you will make a payment to the for-profit to produce cultural performances of the kind you promote, you are probably ok so long as the payment is reasonable.  A charity can take out a full-page advertisement in a for-profit newspaper to promote its charitable program.  So, if all you are doing is paying to assure that cultural programs of your culture are being presented, it should be ok.  (If the show will go on without your sponsorship, you might want to consider why you are paying the for-profit just to get your name out there.)

The term “partner,” however, usually implies some sort of working together, something like a joint venture, where each partner has some say in how the activity is conducted.  The IRS takes the position that if a charity enters into a joint venture with a for-profit, the entire activity (and any income received from it) will be treated as unrelated business activity unless the charity “controls” the joint venture so that it can assure that the charitable activities are paramount.  (See Ready Reference Page: “IRS Says Charities Must Control Joint Ventures”)  Therefore, if you are entering some type of agreement for joint activity, it could be unrelated business activity if you don’t control the operation.  Some unrelated activity is ok, but ultimately a charity could lose its exemption if unrelated activity constitutes a substantial portion of its activity.  (See Ready Reference Page: “Nonprofits Often Worry About UBIT”)

Before you enter into a relationship with the for-profit, figure out exactly what it is so that you can be sure what you are doing is ok.