27680 is a product of a power of 2 and two 4k+1 primes and so it can be expressed a sum of two squares in two different ways viz. 28^2+164^2 and 76^2+148^2.
27680 is a member of OEIS A030117: number of triangles a queen can make (starting anywhere) on an n X n board, here n=24.
The sequence can be generated from n=3 as follows (for n=2, the value is 4):
INPUT
L=[]
for n in [3..30]:
if is_odd(n):
number=13*binomial(n,3)+5*binomial(n,2)
L.append(number)
else:
number=13*binomial(n,3)+5*binomial(n,2)-n/2
L.append(number)
print(L)
OUTPUT
[28, 80, 180, 332, 560, 864, 1272, 1780, 2420, 3184, 4108, 5180, 6440, 7872, 9520, 11364, 13452, 15760, 18340, 21164, 24288, 27680, 31400, 35412, 39780, 44464, 49532, 54940]
27680 is an untouchable, gapful, practical, abundant, Zumkeller & pseudoperfect number.
27680 can form a digit equation as follows:
2 x 7 = 6 + 8 + 0