Electron spin resonance spectra were obtained by electrical detection in a remotely Si-doped 400 nm wide GaAs/AlAs digital parabolic quantum well, yielding $g=\ensuremath{-}0.423$ and $g=\ensuremath{-}0.405$ in perpendicular and parallel fields of 5 T, respectively. The tilt angle dependence of $g$ in the wide parabolic quantum well is qualitatively different from the previously reported $g$-factor anisotropy in narrow GaAs quantum wells. The $g$-factor angle dependence, together with the electrically detected electron-nuclear double resonance spectra, indicate that the spin resonance signals originate mainly from the center of the well. Furthermore, the nuclear spin relaxation in the three-dimentional electron gas (3DES) is found to be independent of temperature in the 1.5--5 K range, while the Korringa law is observed in the 2DES.