27378 is a product of 2, a 4k+3 prime (3) raised to an even power (4) and a 4k+1 prime (13) raised to the power 2 and so it can be expressed as a sum of two squares in exactly two ways viz. 63^2+153^2 =117^2+117^2.

27378 is a member of OEIS A287682: triples of practical numbers: numbers n such that n-2, n, n+2 are all practical numbers. See blog post Practical Numbers. The sequence begins:

4, 6, 18, 30, 198, 306, 462, 702, 1482, 2550, 3330, 4422, 5778, 6102, 6498, 9042, 11178, 11778, 14418, 15498, 17298, 17442, 19458, 20862, 21582, 22878, 23322, 23550, 25230, 26622, 26862, 26910, 27378, 30210, 34542, 36738, 38610, 39006, 39102, ...

27378 is an ABA number since it can be written as A⋅BA, here for A=2, B=117.

27378 is a Harshad number since it is a multiple of its sum of digits (27).

27378 is an abundant and pseudoperfect number.

27378 can be represented as a digit equation, specifically as

(2 - 7) * -3 = 7 + 8.

27378 stabilises after about 440 generations into a glider, a traffic light, a blinker and a variety of still lifes.