Upper-right: (2n-1)²
Upper-left : (2n-1)² - (2n-2)
Lower-left : (2n-1)² - 2(2n-2)
Lower-right: (2n-1)² - 3(2n-2)

Total (nth spiral): 4(2n-1)² - 6(2n-2)
Spirals: ceiling(1001/2) = 501
Sum_{n=2}^{n=501} 16n²-28n+16 = 669 171 000

Answer = 669171001