Does the Bible say for sure that Daniel was a eunuch?
Of course the Bible does not say for sure that Daniel was a eunuch. But, in view of the evidence set out below, I feel sure we can be tolerably certain that he and his three friends were indeed all eunuchs.
If Daniel was a eunuch then there are plausible reasons why the Holy Spirit might have chosen to conceal it. The law in Leviticus 21:20 and Deuteronomy 23:1 declares that a eunuch could neither act as a priest nor enter the congregation. This probably means what the Good News Bible says:
No man who has been castrated ... may be included among the LORD's people. (Deuteronomy 23:1, GNB).
At least, eunuchs could not have an active role in the religious life of the nation. So if the book of Daniel openly revealed that Daniel was a eunuch it, amongst many Jews, would have undermined Daniel's status as a prophet and as a man of God, and consequently undermined the book of Daniel as the word of God.
It was common practice for the later Assyrian, Babylonian and Persian Empires to take the best boys from conquered nations as tribute. In the process the boys would be castrated/made eunuchs. These boys would be trained up to be administrators/civil servants in the royal palaces. They could rise to very high positions of authority and power. The practice was so common there was even a high position in these Empires: eg in the Babylonian Empire the Rab-saris, the Chief of the Eunuchs, who would very likely be a eunuch himself.
As an example of this common practice, Herodotus recounts that in the days of the Persian King Darius, the annual tribute of the 9th satrapy, which included Babylonia and parts of Assyria, to King Darius included "500 child eunuchs" (Herodotus, book 3, note 92). Every year then these 500 boys would have entered into training for the royal court many of them in order to be ready to act as administrators in the king's service. And this extra-biblical evidence is precisely in harmony with the events surrounding the captivity of Daniel and his companions.
Herodotus mentions eunuchs on several occasions in his works, for example:
"And now their generals made good all the threats wherewith they had
menaced the Ionians before the battle. For no sooner did they get
possession of the towns than they choose out all the best favoured
boys and made them eunuchs, while the most beautiful of the girls
they tore from their homes and sent as presents to the king [suggestive of the events in the book of Esther], at the
same time burning the cities themselves, with their temples. Thus were the Ionians for the third time reduced to slavery; once by the Lydians, and a second, and now a third time, by the Persians." (Book 6, note 32).
And eunuchs are spoken of as men in positions of trust and authority, for example:
"I sent my most trusted eunuchs" (Herodotus, Book 1, note 117).
The practice was to ensure that such men would be trusted amongst the royal harem and women at the court. Eunuchs would be able to devote all their time to serving the royal interests because there would be no divided loyalty with neither wife nor family making demands on their time.
The Persians learned the practice from the Babylonians who in turn took it from the Assyrians.
It is, in my mind, inconceivable that Daniel, Shadrach, Meshach and Abednego were not treated in what at the time would have been considered normal practice, which explains why the one in charge over them was the Rab-saris, the Chief of the Eunuchs.