Checking for sum of [1,2,...n] is NOT enough for a perfect solution,
eg. your program gives True for

{ 5,5,5 5,5,5 5,5,5 }
{ 5,5,5 5,5,5 5,5,5 }
{ 5,5,5 5,5,5 5,5,5 }

{ 5,5,5 5,5,5 5,5,5 }
{ 5,5,5 5,5,5 5,5,5 }
{ 5,5,5 5,5,5 5,5,5 }

{ 5,5,5 5,5,5 5,5,5 }
{ 5,5,5 5,5,5 5,5,5 }
{ 5,5,5 5,5,5 5,5,5 }
which obviously is an invalid sudoku of 1,2,...,9
(but it does have sum of 45 in every row, column, and small square)

You have to make statistics of the occurred elements too to determine if the solution is valid.

Your idea basically is nice, but it has one flaw:

• checking for sum of [1,2,...n] is NOT enough for a perfect solution,

eg. your solution gives True for

{ 5,5,5 5,5,5 5,5,5 }
{ 5,5,5 5,5,5 5,5,5 }
{ 5,5,5 5,5,5 5,5,5 }

{ 5,5,5 5,5,5 5,5,5 }
{ 5,5,5 5,5,5 5,5,5 }
{ 5,5,5 5,5,5 5,5,5 }

{ 5,5,5 5,5,5 5,5,5 }
{ 5,5,5 5,5,5 5,5,5 }
{ 5,5,5 5,5,5 5,5,5 }
which obviously is an invalid sudoku of 1,2,...,9
(but it does have sum of 45 in every row, column, and small square)

You have to make statistics of the occurred elements too to determine if the solution is valid.

"The function accepts an integer and returns an integer"
Solution does not work for negative integers (result is always a positive integer due to b * b)

"The function accepts an integer and returns an integer"
Solution is very compact but unfortunately
does not work for negative integers ('-' sign converted to '1')