There are a couple of attestations of this: 2 Maccabees, Valerius Maximus, and Ctesias. Ctesias describes it as such in his 4th century History, quoted by Photius:

At the suggestion of Parysatis, he endeavored by trickery and solemn promises to win over Secydianus. Menostanes did all he could to prevent Secydianus from putting faith in these promises or coming to terms with those who were trying to deceive him. In spite of this Secydianus allowed himself to be persuaded, was arrested, thrown into the ashes, and died, after a reign of six months and fifteen days.

Valerius Maximus describes (if someone could translate these I would be very grateful):

ext.6 Ochus autem, qui postea Darius appellatus est, sanctissimo Persis iure iurando obstrictus ne quem ex coniuratione, quae septem magos cum eo oppresserat, aut veneno aut ferro aut ulla vi aut inopia alimentorum necaret, crudeliorem mortis rationem excogitavit, qua ~ hosustos sibi non perrupto vinculo religionis tolleret: saeptum enim altis parietibus locum cinere conplevit superpositoque tigno prominente benigne cibo et potione exceptos in eo conlocabat, e quo somno sopiti in illam insidiosam congeriem decidebant.

ext.7 Apertior et taetrior alterius Ochi cognomine Artaxerxis crudelitas, qui Atossam sororem atque eandem socrum vivam capite defodit et patruum cum centum amplius filiis ac nepotibus vacua area destitutum iaculis confixit nulla iniuria lacessitus, sed quod in his maximam apud Persas probitatis et fortitudinis laudem consistere videbat.

And Maccabees:

But the King of kings [God, I guess?] aroused the anger of Antiochus against the scoundrel. When the king was shown by Lysias that Menelaus was to blame for all the trouble, he ordered him to be taken to Beroea* and executed there in the customary local method. There is at that place a tower seventy-five feet high, full of ashes,* with a circular rim sloping down steeply on all sides toward the ashes. Anyone guilty of sacrilege or notorious for certain other crimes is brought up there and then hurled down to destruction. In such a manner was Menelaus, that transgressor of the law, fated to die, deprived even of burial. It was altogether just that he who had committed so many sins against the altar with its pure fire and ashes, in ashes should meet his death.

I think that basically exhausts the early primary source material. A priori, there are some things that make me sceptical of this, especially of the interpretations (found in e.g. Bible glosses) that supposes it was smouldering ash. While we know far too little about the religious practices of the Achaemenians, Herodotus does confirm that cremation was against the custom of the Persians in his discussion of Cambyses. Indeed in the extant Avestan literature, the burning of a corpse is alluded to as one of the most heinous crimes there is, since it pollutes both the fire and the earth. Similarly, ashes are considered some of the most ritually pure substances there is. Though Achamaenian monarchs evidently followed the Near Eastern custom of being embalmed [which would be considered a heinous sin in extant Avestan literature] rather than burial by exposure, this should probably be taken as a remarkable but conceivable exception to custom (according to e.g. Mary Boyce), which is especially believable if we suppose Cyrus and his immediate family weren't Persian, which is plausible.

The descriptions given of the tower in Maccabees sounds like it could plausibly be a maybe slightly mangled description of Zoroastrian fire temples. Ctesias' work, composed contrary to what one might expect, is famously unreliable but was favoured by ancient authors. Given this, my suspicion is that it might have been a gruesome torture method imagined by the Greeks (maybe Ctesias himself, just to make his clever anecdote of Darius II's trickery work), based on knowledge of the Persian fire temple cult and their buildings with great fires and sacred ashes. This seems to be supported by Maccabees' mention of the "pure fire and ashes" (the author of which could plausibly simply be transposing tales of the Achaemenian empire onto the Seleucids).

While this type of ironic punishment might have seemed suitable to Ctesias, or to Jews in the 1st or 2nd centuries BC, I really don't think a Persian monarch would have found it anywhere near as amusing.