Translation:It took three days.
間 [かん] means a time-period. It's the difference between "the third" and "three days". You use the same for hours of the day. "一時間" means the duration/period of one hour, while "一時" means one o'clock. As such, it matters.
I've asked a native speaker and I wouldn't say it's still right, since the answer I got was that they never say it without 間. It's like saying "three breads" instead of "three loaves of bread" I guess.
If you meant that as a question, the answer is "no" (as far as I understand as a learner).
三日, in this context (and any other context), is みっか.
三日間 is みっかかん too.
The only times when it becomes さんにち:
- When it's part of a longer number, such as 十三日 (じゅうさんにち, "thirteen days").
- When it's part of a listed range of days, such as 二三日 (にさんにち, "two or three days").
Whether or not さんにち might be a non-standard variant way of saying just 三日 though, I have no idea. However, みっか definitely isn't incorrect in this sentence. ^^