  We present a detailed view of cluster formation (CF) to trace the evolution
and interaction history of the Magellanic Clouds (MCs) in the last 3.5 Gyr.
Using the \textit{Gaia} DR3 data, we parameterized 1710 and 280 star clusters
in the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC), where
847 and 113 clusters are newly characterized in the outer LMC and SMC,
respectively. We estimated the age-extinction-metallicity-distance parameters
using an automated fitting of the color-magnitude diagram (CMD) after field
star removal, followed by an MCMC technique. We report a first-time detection
of two synchronized CF peaks in the MCs at 1.5$\pm$0.12 Gyr and 800$\pm$60 Myr.
We recommend that the choice of the metallicity ($Z$) values of isochrones for
clusters with age $\le$ 1 - 2 Gyr are Z$_{\text{LMC}}$ = 0.004 - 0.008 and
Z$_{\text{SMC}}$ = 0.0016 - 0.004 for the LMC and SMC, respectively. We found
evidence for spiral arms in the LMC, as traced by the cluster count profiles
over the last 3.5 Gyr. The density maps provide evidence of ram-pressure
stripping in the North-East of the LMC, a severe truncation of CF in the South
of the LMC, and a radial shrinkage of CF in the SMC in the last 450 Myr. The
last SMC-LMC interaction ($\sim$ 150 Myr) resulted in a substantial CF in the
North and Eastern SMC, with a marginal impact on the LMC. This study provides
important insights into the CF episodes in the MCs and their connection to the
LMC-SMC-MW interactions.
