Question 863255
quadratic series is n^2 + 2n + 2 as you discovered
to find the sum of the first 21 patterns, we need to break this apart
(sum)n^2 + (sum)2n + (sum)2, all from 1 to 21
we know the sum for the power series n^2 is
(n(n+1)(2n+1))/6
the sum for 2n is the sum of even integers 
n(x1+xn)/2
the sum of 21 "2"'s is
21*2
now we can put it all together
(21*22*43)/6 + 21*(2+42)/2 + 42 = 3815
you need 3815 blocks