Taking the third power of a number is called taking its cube.
Three is the only number to be both a Mersenne prime and a Fermat prime. It is also a Mersenne prime exponent producing the prime 7. The next exponent is 5, the next Fermat prime is 5, and the next Mersenne prime is 7.
3 is in a twin prime pair with 5.
Three is the second lucky number, between 1 and 7.
Testing if a number is a multiple of 3 is as easy as adding up the digits and seeing if they add to a multiple of 3. So 59604 is a multiple of 3 since its digits add to 24, which is a multiple of 3.