We investigated certain properties of cumulative entropy related to the lifetime of consecutive $k$-out-of- $n$:F systems. First, we presented a technique to compute the cumulative entropy of the lifetimes of these systems and studied their preservation properties using the established stochastic orders. Furthermore, we derived valuable bounds applicable in cases where the distribution function of component lifetimes is complex or when systems consist of numerous components. To facilitate practical applications, we introduced two nonparametric estimators for the cumulative entropy of these systems. The efficiency and reliability of these estimators were demonstrated using simulated analysis and subsequently validated using real data sets.