A number that is approximately 6.60568 x 10^16, since that is the best approximation my calculator will give me

The 363 rd triangular number is 66,066 .  Both of these numbers are palindromes.

The 363,474,363 rd triangular number is 66,056,806,460,865,066 .  Both of these numbers are palindromes.

The number in the title is the sum of these four numbers.

(A triangular number is a number that forms a triangle.  Like bowling pins.)