I was going to say the same thing, but then I realised the initial claim was also about 'cultural unity'. So fair enough, and yes a lot of Europe (or all of it in a few sections) has been culturally unified since time immemorial.
It is a bit more complex though, certainly even today there's some very distinct 'culture' in different regions across India. But also shared themes and roots (e.g. Sanskrit & texts written in it, from which modern 'distinct' languages/beliefs/teachings have been derived) that kumarvr's far better placed to comment on than I am.
Not the GP but I'll be more concrete in the other direction.
The Roman Empire is located in Europe, is more recent than "time immemorial", and I'll claim that they didn't regard the various barbarians in Europe outside its sphere of influence as culturally unified with them.
To go even further: I imagine if the Arab world was politically unified with Europe today, there'd be a lot of people saying that it was always a unified Mediterranean cultural entity, sharing Monotheistic Abrahamic religions, Greek intellectual foundations, and having a long-term shared history in the Roman world. It's not a point of view commonly encountered today, though, probably because Europe and the Arab world aren't politically unified.
That is to say, if you decide that a region should be seen as unified (perhaps because of modern political boundaries), one can cherry-pick common elements to try to reach that conclusion. It's not entirely incorrect, but it's a biased way of presenting the evidence in order to justify a preconceived belief.
It is a bit more complex though, certainly even today there's some very distinct 'culture' in different regions across India. But also shared themes and roots (e.g. Sanskrit & texts written in it, from which modern 'distinct' languages/beliefs/teachings have been derived) that kumarvr's far better placed to comment on than I am.