  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 5 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 anti-correlation
with a Pearson correlation coefficient of $r=-0.84\pm0.05$ 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, 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.
