We study the one-shot and concurrent hitting for the discrete-time Grover-coined quantum walk on cubelike graphs G=Cay(\mathbb Z_2^d,\Omega) of degree \Delta=|\Omega|. Starting from the vertex labeled 0, we identify $\sigma=\bigoplus_{\om
We study the one-shot and concurrent hitting for the discrete-time Grover-coined quantum walk on cubelike graphs G=Cay(\mathbb Z_2^d,\Omega) of degree \Delta=|\Omega|. Starting from the vertex labeled 0, we identify \sigma=\bigoplus_{\omega\in\Omega}\omega as a natural target vertex; for the hypercube, \sigma is precisely the antipodal vertex. For families with \Delta\to\infty, let T be an integer having the same parity as \Delta and satisfying \left|T-\frac{\pi\Delta}{2}\right|\leq 1. We show that the probability p_T(\sigma) of finding the walker at \sigma when it is measured at time T satisfies $ p_T(\sigma)=1-O(\Delta^{-1/5}). Thus the target is found with probability tending to one after \Theta(\Delta)$ steps. For the concurrently measured walk, let H_T^{Conc}(\sigma) denote the probability that the target is detected at or before time T when it is tested after every step. We prove $ p_T(\sigma)\leq T H_T^{Conc}(\sigma), which implies H_T^{Conc}(\sigma)=\Omega(\Delta^{-1})$ over the same time scale. The proof uses the Walsh-Fourier decomposition, an exact two-dimensional reduction of each Fourier mode, and a universal second-moment identity for the associated character sums. Our results extend Kempe's hypercube hitting phenomenon (J. Kempe, Probab. Theory Relat. Fields 133, 215-235, 2005) to arbitrary cubelike generating sets and establish the conjectured asymptotic hitting behavior for cublelike and augmented cubes in Mulherkar, Rajdeepak and Sunitha (Int. J. Quantum Inf. 20,2250020, 2022)