Piacere in terms of "I like _" is tricky! One way to deal with this is to always think : "_ is pleasing to me" -- that is the Italian construction. In this form piacere agrees with the thing that you are liking, and is only conjugated in the 3rd person singular or plural. So --
We like the cultural weeks (what is a cultural week???) = The cultural weeks are pleasing to us. Here, "to us" = a noi = ci (indirect object). so you could say "a noi piacciono . . ", or more commonly, "ci piacciono" (piacciono agrees with the cultural weeks). If it were just one week, it would be "ci piace la settimana culturale.
Here is a better explanation: http://my.lifeinitaly.com/threads/7133-the-verb-piacere
Please correct me if I am wrong. The subject and object don't need to be all in the plural form. I believe. Ci = us, therefore piacciono -- Duo means that "we like the cultural weeks." i.e., "the weeks of cultural events." It could have said: "ci piacciono la settimana culturale", (we like the cultural week,) or, "mi place le settimane culturali.," (I like the cultural weeks) for example.
That's not how piacere "works". Piacere agrees with the thing or things being liked. So "I like" or "We like" does not affect "piacere". In english "we like things". In Italian "things please us". Sorry, I never learned my grammar labels.
Think of it like this:
Mi piace la settimana culturale = The cultural week pleases me. "he/she/it pleases" = piace.
Mi piacciono le settimane culturali = The cultural weeks please me. "they please" = piacciono.
Hope this helps.