There may have been multiple ‘epic cycles’; the Trojan one is the best attested one, starting with the Kypria and ending with the Telegony.

Eumelos’ Titanomachy may have been part of a cycle, but the presence of a Titanomachy in the Trojan cycle is not well attested — and if it is, then there are several other poems that are also linked to a ‘cycle’ which have a stronger claim — the Danais, Oidipodea, and Thebaid, for a start (test. 2 ed. Bernabé = Tabula Iliaca 10K, also known as the Tabula Borgia; this is one of the two sources that links a Titanomachy to a cycle).

There is only one ancient literary source where we can be confident in saying that it retells material from the Epic Cycle, and that’s the set of summaries collected by Proklos. Apart from them, there are only three extant writers who we can be confident were directly acquainted with any of the lost epics: Herodotos, Aristotle, and Pausanias. Much of the Cycle may have been lost by the 1st century BCE; it was certainly lost long before Quintus of Smyrna came along a few centuries later. There is no doubt that his retelling was based on summaries similar to the ones we still have today; it is possible (I think overwhelmingly likely) that the same is true for cyclic material in Vergil’s Aeneid and Ovid’s Metamorphoses. There’s a slightly stronger case for Horace being directly acquainted with parts of the cycle, but only slightly, and he doesn’t re-use it in his own poetry.
Quintus’ Posthomerica (date uncertain, but late antique) is fine for the three epics you mention, in the sense that it’s based on the same material we still have today; Quintus also takes material from Ovid. Ovid himself retells bits of the Trojan War in books 12 and 13 of the Metamorphoses (1st cent. BCE-1st cent. CE).

Then there’s Kollouthos, a.k.a. Colluthus, who wrote a Rape of Helen (ca. 500-520 CE), which could be said to correspond to part of the Kypria; and Tryphiodoros wrote a Sack of Ilion (later than 400 CE, but we don’t know how much later), whose beginning and end correspond pretty well to the start and end of the cyclic epic. Both of these are in classical hexameter, emulating Homeric style in some respects.

Another more thorough answer is Tzetzes’ Iliaka, in three parts: the Antehomerica, Homerica, and Posthomerica, in classical hexameter (12th cent.). Unlike the ones mentioned above, Tzetzes’ poems don’t draw from the cyclic summaries, but rather from accounts of the Trojan War in early Byzantine historiography (John Malalas’ Chronography, book 5; John of Antioch’s lost history). The Antehomerica begins with the upbringing of Paris, so you could say that poem as a whole is a sort of parallel to the lost Kypria. The Posthomerica ends with the departure of the Greeks after the destruction of Troy.

There are no extant poetic treatments of the Nostoi and Telegony. But Odysseus’ death at Telegonos’ hands is briefly narrated in two poems: Lykophron’s Alexandra, lines 799-811 (3rd cent. BCE), and Oppian’s Halieutika or ‘on fishing’, book 2 lines 497-505 (2nd cent. CE?).
As well as Tzetzes, there’s another Byzantine-era poem that uses the same historiographical material in a poem: Konstantinos Manasses’ Breviarium Chronicum, lines 1108-1474, in mediaeval dialect and the mediaeval political metre (also 12th cent.). For that matter, there’s also Benoît de Sainte-Maure’s Roman de Troie (12th cent.), which is based on an older form of the same material, but is much much MUCH more expansive. But I’d better emphasise that Tzetzes, Manasses, and Benoît did not draw on the Cycle summaries at all: they’re a completely separate branch of the tradition of the Trojan matter.