Which of the following phrases are correct?
"Faulhaber formula" or "Faulhaber's formula"
"Faulhaber formula" on its own is not good, because it's not grammatical. "The Faulhaber formula" is at least grammatical.
The question is then: should you put "the" before the name, or should you use a possessive? Usage varies, and sometimes you may see both forms.
I see that Wikipedia's article is named "Faulhaber's formula", so I would go with that.