The Capitol. The Kansas Capitol in Topeka is one of the most beautiful State Capitols in the country. It was constructed over a period of 37 years, from 1866 to 1903, at a total cost of $3.2 million.The state government of Kansas has been based in Topeka since the year that Kansas became a state, 1861. The first capital of Kansas was Fort Leavenworth, where territorial governor Andrew Reeder had his headquarters.t was constructed over a period of 37 years, from 1866 to 1903, at a total cost of $3.2 million. The state government of Kansas has been based in Topeka since the year that Kansas became a state, 1861.