708 = 2 x 2 x 3 x 59.
708 is the maximum value of n so that there exist four denominations of stamps so that every postage from 1 to n can be paid for with at most 12 stamps (A001209).
708 is a decagonal pyramidal number (A007585).
708 is the number of different equations that can be made by summing numbers from 1 to 10 and using every number not more than once (A161943).
708 is the sum of the first 29 composite numbers (A053767).
Source: What's Special About This Number?