This paper presents a new approach for spatio-temporal road traffic forecasting that relies on the adoption of the NeuCube architecture based on spiking neural networks. The NeuCube platform was originally conceived and designed to process electroencephalographic (EEG) signals considering their temporal component and their spatial source within the brain. Its neural representation allows for a visual analysis of connectivity among different locations, and also provides a prediction tool harnessing the predictive learning capabilities of dynamic evolving Spiking Neural Networks (deSNNs). Taking advantage of the NeuCube features, this work focuses on the potential of spatially-aware traffic variable forecasts, as well as on the exploration of the spatio-temporal relationships among different sensor locations within a traffic network. Its performance, assessed over real traffic data collected in 51 locations in the center of Madrid (Spain), is superior to that of other machine learning techniques in terms of forecasting accuracy. Moreover, we discuss on the interactions and relationships among sensors of the network provided by Neucube, which may provide valuable insights on the traffic dynamics of the city under study towards enhancing its management.