Michelangelo bought a large block of marble 8 feet tall
to carve a giant Hercules statue. It was unusal at the time
for a sculptor to buy and carve a statue without
a patronage. Michelangelo last job was creating
a snow sculpture for Piero's palance.
Michelangelo sold the statue to the Strozzi family where it remained for many years in the family's palace Palazzo Strozzi. During the seige of Florence in 1530 by Charles V, the statue was sent to the King of France, Francis I, According to Vasari, Giovanbattista della Palla, a agent of the Medici family, sent it to the French King Francis I.
The statue was put in the Fontainebleau Palace. At the Fontainebleau, the statue formed part of a fountain. It stood originally in the Cour de la Fountaine, but was moved to the Jardin de l'Etang. When this garden vanished in 1714 the statue vanished, probably into some fat cat's palace.
It is questionable if Francis I ever owned the Hercules. In a letter dated August, 1546, Francis I wrote to Michelangelo he stated that he did not "possess any sculptures by the master"
In 1977, the art magazine "Burlington Magazine", suggested that the Hercules was transported by della Palla, in 1530, to the Strozzi family house (or bank) in France. The statue was then later donated to King Henry II by a Strozzi family descendent after he became king in 1547.
Read that story here.
Israel Sylvestre made a sketch (in France?) of the statue as did Raphael in Italy.