<p>In this paper, we propose efficient mixed Legendre spectral methods for solving biharmonic equations and time-dependent fourth-order problems on <i>d</i>-dimensional hypercube domains. By constructing a set of simultaneously orthogonal basis functions, the discrete systems are diagonalized. Consequently, both the exact solutions and the approximate solutions can be represented in the form of infinite and truncated Fourier-like series. Furthermore, we develop efficient space-time spectral methods for fourth-order parabolic problems by combining the mixed Legendre spectral method for spatial discretization with the Legendre–Gauss collocation method for temporal discretization. This approach can be implemented in a synchronous parallel manner, enhancing computational efficiency. Rigorous error estimates are provided to establish the theoretical foundation for these methods. Numerical experiments demonstrate that the proposed approaches achieve high-order accuracy and substantially improve computational efficiency, making them highly effective for solving high-dimensional fourth-order problems.</p>