Squaring numbers made up of 6s

1. Choose a a number made up of sixes.
2. The square is made up of:
   1. one fewer 4 than there are repeating 6's
   2. 3
   3. same number of 5's as 4's
   4. 6

Example:

1. If the number to be squared is 666
2. The square of the number has:
   4's (one less than digits in number) 4 4
   3 3
   5's (same number as 4's) 5 5
   6 6
3. So 666 × 3666333 = 443556.