Niall has already read 100 pages of a 520-page book. To find out how many pages he has left to read, we calculate:
\[ 520 - 100 = 420 \]
Niall plans to read 60 pages per night. To determine how many nights it will take him to finish the remaining 420 pages, we divide the number of pages left by the number of pages he reads per night:
\[ \frac{420}{60} = 7 \]
Therefore, it will take Niall 7 nights to finish the book.