Sum to Infinity

Normal sudoku rules apply.

The grey lines are palindromes (they read the same in either direction) that both exclude the digit 8.

A single 8 resides inside each loop of the infinity (∞) symbol; all other digits appear along that symbol.

The sum of the digits along the summation (Σ) symbol is a square number, though no individual digit is a square.

All digits on the summation symbol appear in the square (2x2) cage.

The sum of digits in the smaller (1x2) cage is a square.

Digits along the indicated diagonals must sum to the given total.

Digits separated by a white dot are consecutive.