The cueing task is one of the most prominent paradigms to study covert attention. Observers are quicker and more accurate in detecting a target when it appears with a cue (valid trials) than when it appears opposite to the cue (invalid trials). How neuronal populations of cells across the visual hierarchy progressively represent and integrate visual information across the target, cues, and locations to give rise to the behavioral cueing effect is not well understood. To gain a theoretical understanding of the plausible system-wide neuronal population statistics, computations, and mechanisms mediating the cueing effect, we analyze the response properties of 180k neurons per network across layers of ten feedforward Convolutional Neural Networks (CNN). The CNNs are trained from images with luminance noise, without any explicit incorporation of an attention mechanism, and show human-like beneficial influences of cues on detection accuracy. Early visual hierarchy layers show retinotopic neurons separately tuned to target or cue with excitatory or inhibitory responses. Later layers show neurons that are jointly tuned to both target and cue and integrate information across locations. Consistent with physiological findings, we find an increased influence of the cue on target responses in higher layers (areas) in the network and computational stages similar to those of a Bayesian ideal observer, but with more gradual transitions. The cue influences the mean neuronal response to the target and distractor, and changes target sensitivity with two mechanisms: integration of information across locations at the dense layer with neurons more driven by the cued location, and an interaction with the thresholding Rectified Linear Activation Unit (ReLU) in the last convolution layer. We find novel neuronal properties not yet reported in physiological studies: the presence of cue-inhibitory neurons, inhibitory cue influences on target neurons, location-opponent cells, and higher sensitivity to the cue in intermediate layers than later layers. Together, our analyses illustrate a system-wide analysis of the brain computations that might give rise to behavioral cueing effects and provide a theoretical framework to inform neurophysiological studies.