What is the declension is the Latin word syllabus? I've heard it's first declension, but I think that was simply on the presupposition that it was a Greek loan and not necessarily because it actually appears in the corpus as first declension… Anyone know?

The spelling syllabus came from a fifteenth-century edition of Cicero’s Letters to Atticus where it is a misspelling of a form of the word sittybus, which refers to a strip of parchment. However, now syllabus is thought of as a Neo-Latin word with a plural form syllabi, so it is a second-declension masculine noun.

If you chose to use “syllabi” in English, and someone says it is wrong, you could say that the word is now, regardless of its origins, a Neo-Latin word, and such a plural may be formed.

From Plûrâlitâs Latîna