Assuming interest rates are constant the forward price of the future is equal to the forward price of the forward contract with the same strike and maturity.
The difference between the spot and the forward price is the forward premium or forward discount, generally considered in the form of a profit, or loss, by the purchasing party.
Since these occur at different times, and are difficult to predict, estimation of the forward price can be difficult, particularly if there are not many stocks in the chosen index.
In other words, the rational forward price represents the expected future value of the underlying discounted at the risk free rate (the asset with a known future-price, as above).
In the language of stochastic processes, the forward price is a martingale under the forward measure, whereas the futures price is a martingale under the risk-neutral measure.