Q: Is it permissible to make up missed days of Ramadan during the 10 days of Dhul-Hijjah or the first 10 days of al-Muharram? What about Ashura, etc.?
A: The 10 days of Dhul-Hijjah are days of worship and so it is not disliked to make up any missed days of Ramadan during that time. In fact, in the event that they still remain, it was reported that Umar (radi Allahu 'anhu) preferred making them up then.
The first 10 days of al-Muharram, which include Ashura, are similar. They are days of worship, virtue, and increased reward and thus it is not disliked to make up missed Ramadan fasts then.
Because it is not permitted to embark upon voluntary fasting before making up Ramadan, which requires a definitive intention, it is absolutely crucial if you fast during these days to make your intention for the missed days of Ramadan and not for those voluntary days or a combination thereof.
Allah knows best.
Source: Sharh al-Muntaha, Kash-shaf al-Qina, Lata'if al-Ma'arif