He was born in Bygland. His father, physician Tycho Fredrik Edvard Castberg, was the oldest living son of Peter Hersleb Harboe Castberg. As such Oscar Ambrosius Castberg was the nephew of Johan Christian Tandberg Castberg and first cousin of Johan and Torgrim Castberg. In addition, Oscar Ambrosius Castberg had one older brother, the banker Peter Harboe Castberg.
Oscar Ambrosius Castberg first tried his luck at sea, but gave this up due to problems with seasickness. Instead, he took a sculptor's education, studying with a public grant under Julius Middelthun in Christiania and Jens Adolf Jerichau in Copenhagen. Due to the difficulty of surviving from sculpting alone, he took up painting as well. He is represented with one work in the National Gallery of Norway.
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