35501

Yes, multiplies of three does have always a consecutive number sum more than three numbers.

For example:
18=5+6+7
21=10+11 and 1+2+3+4+5+6
24=7+8+9
27=2+3+4+5+6+7
30=6+7+8+9 and 4+5+6+7+8

But the multiplies of fours does not have a consecutive number sum more than three numbers.

For Example:
16= has no consecutive number sum.