Math problems!?

Question

1) The smaller of two triangular numbers whose sum & difference are also triangular numbers.
2) The only cube that is one less than a square.
3) The 2 digit number that is divisible by both the sum and the product of its digits
4) The larger number of the fourth set of twin primes
Please help with all or any of these you may know. Thanks!

Answer 1

1. no idea
2. 8 (9-1)
3.12 (12/2 = 6, 12/3 = 4)
4. no idea

Answer 2

1) 15. They are 15 and 21.

2) 8, 1 less than 9.

3) 24 (and 12, as the previous answerer found...and 36....).

4) 19. They are 17 and 19.