Inband full-duplex radio transceivers offer enhanced spectral efficiency by transmitting and receiving simultaneously at the same frequency. However, deployment of such systems is challenging due to the inherent self-interference stemming from coupling of the transmit signal to the receiver. Furthermore, to track changes in the time-varying self-interference channel, the process needs to be self-adaptive. Thus, advanced solutions are required to efficiently mitigate the self-interference. With the current rise in parallel architectures due to limitations of performance enhancement by higher clock frequencies, multi-core platforms are considered as viable solutions for implementing such advanced techniques. This paper describes a progranunable implementation of an adaptive nonlinear digital self-interference cancellation method for full-duplex transceivers on two mobile GPUs and a multi-core CPU. The results demonstrate the feasibility of realizing a real-time software-based implementation of digital self-interference cancellation on a mobile GPU, in case of a 20 MHz cancellation bandwidth.