From the Curious Math site: Curious Calculations.

Not very useful, but certainly curious.

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=12345678987654321

3 x 37 = 111 and 1 + 1 + 1 = 3
6 x 37 = 222 and 2 + 2 + 2 = 6
9 x 37 = 333 and 3 + 3 + 3 = 9
12 x 37 = 444 and 4 + 4 + 4 = 12
15 x 37 = 555 and 5 + 5 + 5 = 15
18 x 37 = 666 and 6 + 6 + 6 = 18
21 x 37 = 777 and 7 + 7 + 7 = 21
24 x 37 = 888 and 8 + 8 + 8 = 24
27 x 37 = 999 and 9 + 9 + 9 = 27