27748 is a member of OEIS A176581: n^3 + smallest square >= n^3. Here is an algorithm that will generate the initial members of this sequence (permalink):

INPUT

L=[]

for n in [0..27]:

  for m in [n^3..(n+1)^3]:

    if is_square(m):

      L.append(n^3+m)

      break

print(L)

OUTPUT

[0, 2, 17, 63, 128, 269, 441, 704, 1041, 1458, 2024, 2700, 3492, 4406, 5553, 6856, 8192, 9954, 11761, 13748, 16100, 18670, 21464, 24488, 27748, 31250, 35265, 39564]

27748 is a member of OEIS A111948: Admirable Harshad numbers n such that the subtracted divisor is equal to the digital sum of n.

Here the divisors are 1, 2, 4, 7, 14, 28, 991, 1982, 3964, 6937, 13874, 27748 and so the subtracted divisor is 28 because this is the SOD of the number.

27748 is an admirable number.

27748 is a hoax number, since the sum of its digits (28) coincides with the sum of the digits of its distinct prime factors.

27748 is a gapful number since it is divisible by the concatenation (28) of its first and last digits.

27748 is a primitive abundant number since it is smaller than the sum of its proper divisors, none of which is abundant.

27748 is a pseudoperfect and Zumkeller number.

27748 has an aliquot sequence that does not terminate after 121 steps.

27748 is an attractor under the ODD(+) and EVEN)-) and EVEN(+) and ODD(-) algorithm, meaning that the sums of its odd and even integers (14) are identical.

27748 can be rendered as a digit equation as follows:

-2 + 7 + 7 = 4 + 8