Big data is generated from various sources, such as the Internet of things, social media, databases, wearables, smart cars, and so on, and is characterized by five V’s: volume, value, variety, velocity, and veracity. Transmitting big data to secondary users (SUs) over a cognitive cloud radio access network (CRAN) offers multiple benefits and critical challenges. To address these limitations, we have designed two deadline-aware, non-preemptive algorithms that maximize the sum of weighted data transferred by the network over admission, time scheduling, spectrum, and remote radio head (RRH) allocation decisions. Each data request can have a different size, target bit error rate (BER), minimum signal-to-noise ratio (SNR) requirement, and deadline, incorporating the simultaneous provision of various types of big data and ordinary data jointly. Furthermore, our formulation considers all five V’s of big data. The first algorithm we propose is an offline batch scheduling (OFB) algorithm, which assumes that all data requests are available at the time of optimization. While this sub-optimal algorithm has a lower complexity and can be implemented in larger networks than the global optimum algorithm, it is not practical for real-time applications since it requires collecting all data requests beforehand for joint scheduling. Thus, our second one is a sub-optimal online real-time scheduling (ONR) algorithm that performs admission and resource allocation on-the-fly using predictions of upcoming data requests and future availability of spectrum channels. After deriving these two algorithms, we conduct a thorough performance analysis and derive bounds on their objective values compared to the global optimum. We then demonstrate their effectiveness in achieving higher weighted sums of transferred data and prioritizing SUs with big data requests over existing alternatives through extensive numerical comparisons.