27476 is a product of a power of 2 and a 4k+1 prime and can therefore be expressed as a sum of two squares in one way only viz. 124^2 + 110^2.

27476 is a member of OEIS A055480: energetic numbers that can be broken into two or more substrings and expressed as a sum of positive powers of those substrings. Here the breakdown is 27^3+4^6+7^4+6^4.

It is 2812th member of this sequence so energetic numbers are relatively common (about 1 in 10) but the trick is to find the relevant substrings. This text file contains a list of the first 10,000 terms of the sequence but the breakdown of the numbers is not given.

27476 can be expressed as a digit equation as follows:

2 + 7 = -4 + 7 + 6