## Step 1: Understand the original gravitational force relationship
In our universe, the gravitational force between two objects is proportional to the inverse square of the distance between them. However, in the imagined universe, the gravitational force is proportional to the inverse cube of the distance. This means if the distance doubles, the gravitational force would decrease by a factor of \(2^3 = 8\), not \(2^2 = 4\) as in our universe.

## Step 2: Calculate the new gravitational force
Given that the gravitational force decreases by a factor of 8 when the distance doubles, if the original gravitational force is F, the new gravitational force when the planet is pushed into an orbit exactly twice as far away would be \(F/8\).

## Step 3: Determine the likely outcome for the planet's new orbit
Considering the drastic decrease in gravitational force, the planet's velocity at the new distance would likely exceed the required velocity for a stable, circular orbit at that distance. This is because the force holding the planet in its orbit is significantly weaker, meaning the planet would not be sufficiently bound to maintain a circular path.

## Step 4: Explain the outcome
Given the gravitational force is now \(1/8\) of what it was, the planet's new orbit would likely become elliptical or possibly even escape the star's gravitational pull if the planet's velocity at the new distance exceeds the escape velocity. The exact outcome would depend on the planet's velocity vector at the moment it was pushed into the new orbit, but remaining in a stable, circular orbit without any additional forces acting upon it would be highly unlikely.

The final answer is: $\boxed{1/8}$