Ta(7) is still not found yet. Maybe we will wait for the super mathematicians for few more years and they get the value of it.
So far, the ever-found biggest Taxicab number is
Ta(6)=24153319581254312065344=5821623+289062063=30641733+288948033=85192813+286574873=162180683+270932083=174924963+265904523=182899223+262243663
Enough mind-blowing isn't it?
~The smartest cookie in the world