Your original latitude, longitude values are 52.516316, 13.377825 respectively. That is not the same as 52Ā°51ā²63ā³ N and 13Ā°37ā²78" E. Your original values are degrees in decimal format. They are equivalent to 52Ā°30ā²59ā³ N and 13Ā°22ā²40" E. For example if your latitude was 52.5, that is equivalent to 52Ā°30ā², since .5 degrees equals 30'.
The issue is you are entering the original values as if they are already degrees / minutes / seconds and THEN changing the format. When you enter the values you have to enter them in the CURRENT format, since that is how they are interpreted. Simply enter the values into the two columns as decimal values (52.516316, 13.377825). Then change the formats to the geographic formats and it will display the values in the new format. Note, the values didn't really change, it is just the way they are being interpreted / displayed.
I created a new data table and entered the lat/lon as decimal values, then I changed the formats. Attached is a Graph Builder plot, showing Brandenburger Tor plotted correctly (notice the little black dot in the center), along with the data table and values in Degrees / Minutes / Seconds format.
Let me know how it goes.