Le $x$ be the arithmetic mean and $y, z$ be the two geometric means between any two positive numbers, then $\dfrac{y^3+z^3}{x y z}=$ -----------

Let the two positive numbers be $a$ and $b$.

The arithmetic mean $x$ is given by $x = \dfrac{a+b}{2}$.

The two geometric means $y$ and $z$ between $a$ and $b$ imply that $a, y, z, b$ are in geometric progression. Let the common ratio be $r$. Then $y = ar$, $z = ar^2$, and $b = ar^3$.

From $b = ar^3$, we have $r = \left(\dfrac{b}{a}\right)^{1/3}$.

The product $y z = (ar)(ar^2) = a^2 r^3 = a^2 \left(\dfrac{b}{a}\right) = ab$.

The sum $y^3 + z^3 = (ar)^3 + (ar^2)^3 = a^3 r^3 + a^3 r^6 = a^3 \left(\dfrac{b}{a}\right) + a^3 \left(\dfrac{b}{a}\right)^2 = a^2 b + a b^2 = ab(a+b)$.

Substituting these into the expression $\dfrac{y^3+z^3}{x y z}$:

$\dfrac{ab(a+b)}{x(ab)} = \dfrac{a+b}{x}$.

Since $x = \dfrac{a+b}{2}$, we have $a+b = 2x$.

Therefore, $\dfrac{2x}{x} = 2$.

Answer: 2