Using the star cluster catalogs from the Hubble Space Telescope program Legacy Extragalactic UV survey (LEGUS) and 8 mu m images from the IRAC camera on the Spitzer Space Telescope for five galaxies within 5 Mpc, we investigate how the 8 mu m dust luminosity correlates with the stellar age on the 30-50 pc scale of star-forming regions. We construct a sample of 97 regions centered at local peaks of 8 mu m emission, each containing one or more young star cluster candidates from the LEGUS catalogs. We find a tight anticorrelation with a Pearson correlation coefficient ofr = -0.84 0.05 between the mass-normalized dust-only 8 mu m luminosity and the age of stellar clusters younger than 1 Gyr; the 8 mu m luminosity decreases with increasing age of the stellar population. Simple assumptions on a combination of stellar and dust emission models reproduce the observed trend. We also explore how the scatter of the observed trend depends on assumptions of stellar metallicity, polycyclic aromatic hydrocarbon (PAH) abundance, fraction of stellar light absorbed by dust, and instantaneous versus continuous star formation models. We find that variations in stellar metallicity have little effect on the scatter, while PAH abundance and the fraction of dust-absorbed light bracket the full range of the data. We also find that the trend is better explained by continuous star formation, rather than instantaneous burst models. We ascribe this result to the presence of multiple star clusters with different ages in many of the regions. Upper limits of the dust-only 8 mu m emission as a function of age are provided.