216

216 is the cube of 6, and the sum of three cubes: 216 = 6 3 = 3 3 + 4 3 + 5 3 . {\displaystyle 216=6^{3}=3^{3}+4^{3}+5^{3}.} It is the smallest cube that can be represented as a sum of three positive cubes,making it the first nontrivial example for Euler's sum of powers conjecture. It is, moreover, the smallest number that can be represented as a sum of any number of distinct positive cubes in more than one way. It is a highly powerful number: the product 3 × 3 {\displaystyle 3\times 3} of the exponents in its prime factorization 216 = 2 3 × 3 3 {\displaystyle 216=2^{3}\times 3^{3}} is larger than the product of exponents of any smaller number.