Lensless scattering imaging is a prospective approach to microscopy in which a high-resolution image of an object is reconstructed from one or more measured speckle patterns, thus providing a solution in situations where the use of imaging optics is not possible. However, current lensless scattering imaging methods are typically limited by the need for a light source with a narrowband spectrum. Here, we propose two general approaches that enable single-shot lensless scattering imaging under broadband illumination in both noninvasive [without point spread function (PSF) calibration] and invasive (with PSF calibration) modes. The first noninvasive approach is based on a numerical refinement of the broadband pattern in the cepstrum incorporated with a modified phase retrieval strategy. The latter invasive approach is correlation inspired and generalized within a computational optimization framework. Both approaches are experimentally verified using visible radiation with a full-width-at-half-maximum bandwidth as wide as 280 nm ($\mathrm{\Delta }\lambda /\lambda =44.8\%$) and a speckle contrast ratio as low as 0.0823. Because of its generality and ease of implementation, we expect this method to find widespread applications in ultrafast science, passive sensing, and biomedical applications.