The short answer is, no; because the phrases translated “forever and ever” don’t include the adjective {aio_nion} (or eonian). The suffixing of the adjective changes sometimes, of course, which can make for confusion.
Some example of related terms and phrases:
1.) The adjective “eonian”, or {aio_nion}, used in Matt 25:41, 46 (as a topically handy example ) to describe what kind of “fire” and “chastening” and what kind of life is being given; {to pur to aio_nion} {kolasin aio_nion} and {zo_e_n aio_nion}, each introduced with the preposition {eis} or “into”.
(The reference to the fire in verse 41 is extremely interesting: the grammatic construction shows that “eonian” is being thought of as a noun reference in parallel identification with the fire. Literally it would be “into the Fire, the Everlasting”. Soooo… how many “Everlastings” are there supposed to exist in all reality?! One One that I am aware of, and acknowledge and profess!! )
Another highly interesting use of the adjective is at 2 Tim 1:9, where the calling and salvation of God are given to us, not according to our works, but given to us in Christ Jesus according to God’s own purpose and grace {pro chrono_n aio_nio_n}. At the very least this has to mean “before eternal times”, which again at the least is a reference going back to the heart of God Himself (as the whole context emphasizes anyway). But if we’re thinking about the adjective {aio_nion} (here suffixed with an omega, not an omicron, in order to match the suffix of {chron-} in its prepositional phrase link with {pro}) being itself a source-reference to God the Everlasting One, then it makes even more sense: the gift of grace occurs in some way superior to the times-from-God. This has the advantage of not requiring us to treat the times themselves as “eternal”, which would be instantly contradictory to the sense of the passage. (Note the relationship of this sentence, as a whole, to a similar statement near the end of Romans, discussed by me elsewhere in its uses of “eonian” as a description of a secret and as a description of God.)
The adjective “eonian” occurs more often than any other form or phrase of the word, but all the other forms or phrases together occur more often (in total) than “eonian”.
The form of the word here, {aio_nio_n}, should not be confused with “eons” in genitive form as an object of the preposition “of”, {aio_no_n}. This has the same basic meaning of ‘a particular segment of natural history’ as “eons” in accusative form as the object of some other prepositions, {aio_nas}.
A good example of both of these put together would be:
2.) “into the eons of the eons” {eis tous aio_nas to_n aio_no_n}. Such as in the doxology of Rev 1:7, “To Him is the glory and the might into the eons of the eons”.
This phrase occurs quite frequently in the NT, especially as a doxology: Rom 16:26, Gal 1:5, Ph 4:20, 1Tim 1:17, Heb 13:21, 1Pet 4:11, 5:11, Rev 1:7 (as noted). There are probably a dozen other uses as well, including Christ (Rev 1:18) and God (Rev 4:9-10, 10:6, 15:7) living “into the eons of the eons”.
Of interest to our present topic, Satan is tormented into the eons of the eons (Rev 20:1); the smoke of the Great Harlot Babylon goes up into the eons of the eons (Rev 19:3); and those who worship the Beast and his Image, receiving the mark on hand or forehead, shall drink the cup of the wrath of God unmixed in the presence of the angels of God and of the Lamb, with the smoke of their torment ascending into ages of ages. (This last has a minor variant where the direct article for {aio_no_n} is omitted.)
Some rare variant phrasings in the NT include:
3.) “the eon of the eons”, {tou aio_nos to_n aio_no_n}, Eph 20:21, “the glory of Him in the congregation and in Christ Jesus into all the generations of the eon of the eons.” (This version has the genitive in both prepositional phrases.)
4.) “the eon of the eon”, {eis ton aio_na tou aio_nos}, Heb 1:8, “The throne of yours, O God, is into the eon of the eon.”
5.) “into all the eon”, {eis pantas tous aio_nas}, Jude 25, “to the only God our Savior through Jesus Christ our Lord: glory, greatness, might and authority, before all the eon {pro pantos tou aio_nos} and into all the eon, Amen!”
6.) “before the eons”, {pro to_n aio_non}, 1 Cor 2:7, “But we speak of God a wisdom in mystery: that which has been hidden, which God designated beforehand, before the eons, into our glory!”
7.) “from the eons”, {apo to_n io_no_n}, Eph 3:9, “the fellowship of the mystery: that which has been hidden from the eons in God Himself, all the things having been created through Jesus Christ.”
8.) “from an/the eon”, {ap-aio_nos}, Acts 15:18, “known (to the Lord in His work) from an eon”. (A few other NT occurrences, too.)
9.) “into an/the eon”, {eis aio_na}, Jude 13, “wandering stars (asteres plane_tai), for whom the blackness of darkness into an eon has been kept.” (Trivia note: “has been kept”, or {tete_re_tai}, sounds rather like a pun for Tartarus, where God thrusts sinning angel/messengers in 2 Pet 2:4.)
More frequent are the phrases:
10.) “into the eon”, {eis ton aio_na}, many examples, Matt 21:19/Mark 11:14; Mark 3:29; John 4:14, 6:51, 58, 8:35, 51-52, 10:28, 11:26, 12:34, 13:8, 14:16; 1 Cor 8:13; 2 Cor 9:9; Heb 5:6, 6:20, 7:17, 21, 24, 28; 1 John 2:17; 2 John 2.
11.) “into the eons”, Luke 1:33, 55; Heb 13:8; 1Pet 1:25; and obviously also all those doxology places listed back under set (2).
While there are several other occurrences of the term “eon” in the NT, these are the ones which tend to be translated “eternal”, “forever”, “everlasting”, etc.
The point (recusing back to Michael’s question) is that the phrasing might be “ageish” (as an adjective–or as a vocative noun, even, per my Matt 25 example!), or it might be “age of the ages”. But it’s never “age of the ageish”.
But the difference between spelling {aio_nion} and {aio_non} (depending on the suffix of the latter, which is usually an omega instead of an omicron, though: {aio_no_n}) is pretty small.
And now, having presented these for consideration and discussion, I am off to eat lunch at last!