In this paper, we present some upper and lower bounds for operator space numerical radius of $k\\\\times k$ block matrices, with entries in $\\\\mathcal{M}_n(X)$, when $X$ is a numerical radius operator space. We also derive formulas for operator space numerical radius of some special bidiagonal block matrices. One of our main results states that if $ (X, (W_n)) $ is a numerical radius operator space and $ x_1, \\\\ldots, x_k \\\\in \\\\mathcal{M}_n(X)$, then \\\\begin{align*} & W_{kn}\\\\left({\\\\rm offdiag}(x_1, x_2, \\\\ldots, x_k)\\\\right)\\\\\\\\ & \\\\leq \\\\frac{1}{k} \\\\max \\\\left\\\\lbrace W_n \\\\left(\\\\sum_{r=1}^{k} \\\\omega^{2r} x_{r} \\\\right), W_n \\\\left(\\\\sum_{r=1}^{k} x_{r} \\\\right)\\\\right\\\\rbrace + \\\\frac{1}{k}\\\\sum_{s=3}^{2k-1} W_n\\\\left(\\\\sum_{r=1}^{k} \\\\omega^{rs} x_{r} \\\\right)\\\\\\\\ & \\\\leq \\\\frac{1}{k}\\\\sum_{s=2}^{2k} W_n\\\\left(\\\\sum_{r=1}^{k} \\\\omega^{rs} x_{r} \\\\right), \\\\end{align*} where $\\\\omega = e^{\\\\frac{2 \\\\pi i}{k}}$ is the $k$-th root of unity.

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