Let W={(x,y,z) ∈ R^3: 1≤x^2+y^2+z^2 ≤ β^2; x,y≥0}. Knowing that the triple integral ∭/W e√(x^2+y^2+z^2)^3 dxdydz is equal to 6π, calculate the value of β^3. Please provide your answer to three decimal places.

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