No
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3610 = 19 * 19 * 2 * 5. Each factor must appear 3 times to be a perfect cube, so multiply by (19 * 2 * 2 * 5 * 5) = 1900. And the perfect cube is 6859000
A perfect cube is the cube of an integer (whole number). This means that, for n to be a perfect cube, n = x3, x∈ℤ Eg. ±1 [=(±1)3], 8 [=(±2)3], ±27 [= (±3)3], etc.
If by cube you mean perfect cube (a cube of an integer), then no, and the nearest perfect cube is 81.
64. 4x4x4 and 8x8
It is a perfect cube.