Namaste Ram11 and all
It is said that the Vedas are apaurusheya which means that they do not have an author. Not only Vedas do not have a human authors, namely that tells that the Rishis (sages) -- those which are said to have been Vedic seers -- received Vedas as a revelation and therefore they are not the authors but only recipients of the Vedic texts, but not even the gods (devas) and even the Supreme God (Vishnu) also were not the authors of the Vedas!
The apaurusheya character of the Vedas (all Shruti texts) simply follows from the fact that they are eternal. Something which is eternal has no beginning and no end in time and therefore can be said that has never been created! If it has never been created then it has no creator or author!
Thus Vedas, Brahman, His holy name and form (holy names such as Vishnu, Rama, Krishna, Shiva, ... , and forms of the Supreme Lord such as four-handed form of Lord Narayana and two-handed form of Lord Krishna, etc), His abode (Vaikuntha, Goloka, Sadasivaloka, ... etc), and also we living beings (jivas) are said to be eternal. Hence all these has never been created!
Sometimes it is said that God created living beings. But that does not mean that He has created the spiritual souls (jivas, jiva souls), but that only means that He created the material bodies of living beings in this material world. In this sense it is not wrong to say that the Lord created living beings, however it would be wrong to think that the Lord created the jiva souls!
So if you want a confirmation from the scriptures about Vedas being apaurusheya then do not ask where in the scriptures is said something like "The Vedas are apaurusheya" because such a statement probably you will not find anywhere, but ask where is stated that Vedas are eternal.
Acaryas usually quote a verse from the Rig Veda 8.75.6 about that:
tasmai nūnamabhidyave vācā virūpa nityayā |
vṛṣṇe codasva suṣṭutim ||
However the Griffith's English translation of this verse is located as verse number 8.64.6 at sacred-texts.com:
"Now, O Virūpa, rouse for him, Strong God who shines at early morn,
Fair praise with voice that ceases not."
I do not know why the discrepancy arises between these two different ways of counting verses.
This part of the verse which Griffith translated as "voice that ceases not" other translators give as "the eternal Vedic speech". Hence the eternality of the Vedas is declared in this verse. From this the apaurusheya character of the Vedas is established.
However sometimes we read statements in the scriptures that say:
"From that great general sacrifice Ṛcas and Sāma-hymns were born:
Therefrom were spells and charms produced; the Yajus had its birth from it." (Rig Veda 10.90.9)
Somebody could say that the above passage proves that the Vedas (Rig Veda, Sama Veda and Yajur Veda mentioned in the verse) were born and, because they were born, must also perish in the end. For this reason the Vedas are not eternal. Hence they are not apaurusheya! Somebody could say that.
But it is not so. The word "born" or "produced" here means "manifested" (not born in the ordinary sense). Thus the Vedas were just manifested or revealed to the Rishis (sages) and to the gods. For this reason it is said that the Vedas are revealed holy scriptures.
The eternal character of the Vedas is also pronounced elsewhere in the scriptures.
It is said in the Srimad Bhagavatam 6.16.51 that the Vedas are called "śabda-brahma" which means "the sound vibration (or voice) of the Vedas", and the same verse says this śabda-brahma is śāśvatī "eternal" (śabda-brahma paraḿ brahma mamobhe śāśvatī tanū). Compare this with the above mentioned Rig Veda vācā virūpa nityayā "voice that ceases not" or "the eternal Vedic speech".
Manu-smriti, chapter 12, says:
94. "The Veda is the eternal eye of the manes, gods, and men"
99. "The eternal lore of the Veda upholds all created beings"
- lore -- accumulated knowledge or beliefs held by a group about a subject, especially when passed from generation to generation by oral tradition
Yes, indeed, Brihadaranyaka Upanishad 2.4.10 says:
Originally Posted by Ram11
'As clouds of smoke proceed by themselves out of a lighted fire kindled with damp fuel, thus, verily, O Maitreyî, has been breathed forth from this great Being what we have as Rig-veda, Yagur-veda, Sama-veda, Atharvâṅgirasas, Itihâsa (legends), Purâna (cosmogonies), Vidyâ (knowledge), the Upanishads, Slokas (verses), Sûtras (prose rules), Anuvyâkhyânas (glosses), Vyâkhyânas (commentaries). From him alone all these were breathed forth.
The same Upanishad in 4.5.11 repeating the same thing and adds:
" ... what is sacrificed, what is poured out, food, drink, this world and the other world, and all creatures. From him alone all these were breathed forth."
So not only the Vedas were breathed forth from the Lord but this whole world (universe), and all creatures (including gods), food, etc.