ok. i see that i couldn't explain my point clearly. maybe "formal" is not the right word to describe it (i have some problems with my english vocabulary). what i try to mean by the formal is that we see its "nocte" form on almost every classical text. and we know that "nox" is a syncopated i-stem word, so the ablative should be "nocte" according to its linguistic properties. but "noctu" was somewise invented by Naevius for certain poetical reasons, at least we know it that way from the survived texts. we can also see that noctu form on the poems of Vergilius, Ovidius etc. that is to say that noctu is an archaic (Naev.+) and poetical form. and i thought that the form which is not poetical could be named as formal.
"Noctu" can be "Nocte" also, according to Dicolatin.
Noctu is given as an older form, around Plautus, 2nd century BC.
The Gaffiot dictionary gives both "Noctu" and "Nocte" for "at night time". (both Noctu and Nocte are ablative singular, but one is the variant of the other)
If the Gaffiot gives both "noctu" and "nocte", with the same meaning, you can trust it, it's a reference.
(And the Gaffiot is so full of details, that I believe that if it was more formal, it would have tell us.)
I would tend to prefer "nocte", because it was listed as the main form by Dicolatin, but when I've checked, I've found a lot of "noctu", here: