76 has a unique representation as the sum of three squares: 76 = 22 + 62 + 62.
76 is the ninth Lucas number. Lucas numbers are the sequence of integers obtained when each successive element is the sum of the previous two elements, starting with 1 and 3.
76 is the number of integer partitions of 21 into distinct parts. The partitions of an integer are the number of ways of writing that integer as a sum of positive integers without regard to order with the constraint that all integers in a given partition are distinct.
Meredith Wilson's song "Seventy-six Trombones" is a highlight of the musical The Music Man.
Source: Wolfram MathWorld