IN SPITE OF and DESPITE are exactly equal in use. DESPITE does not take OF; neither is it preceded by IN. In spite of = Despite = Although

The construction is:

In Spite Of/Despite + Noun/Pronoun
OR
In Spite Of/Despite + Gerund (ing form)

IN SPITE OF my sickness I went to the office. (noun construction)
= DESPITE my sickness I went to the office.

IN SPITE OF being sick I went to the office. (gerund construction)
= DESPITE being sick I went to the office.

NOTE: IN SPITE OF/DESPITE are never followed by a clause; e.g.

INCORRECT: In spite of/Despite she fell midway through the race, she won.
CORRECT: In spite of/Despite falling midway through the race she won.

However, we can use a clause if IN SPITE OF/DESPITE are followed by THE FACT THAT; e.g.

IN SPITE OF/DESPITE the fact that she fell midway through the race, she won.

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