64 = 26.
64 is the first number after 1 to be both a square and a cube: 64 = 82 = 43.
64 is the number of integer partitions of 20 into distinct parts.
64 is 121 in base 7 and 44 in base 15. It is 1000000 in base 2, 1000 in base 4, 100 in base 8, 40 in base 16, and 20 in base 32.
Source: Phillips, R. 1994. Number Facts, Figures and Fiction. Cambridge University Press.
Square numbers that are cube numbers are quite interesting. I believe the next such number is 3^6 which can be written as (3^2)^3 or (3^3)^2 and equals 729. A square number that is a cube number is a number raised to a power that contains a factor of 2 and 3.
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