Using the default precision of UBASIC:

10   Lhs=(2^(1/3)-1)^(1/3)
20   Rhs=(1/9)^(1/3)-(2/9)^(1/3)+(4/9)^(1/3)
30   print Lhs
40   print Rhs

produces

0.6381858208606441523
0.6381858208606441534

which looks like the difference is only rounding error.

This can be confirmed by increasing the precision:

point 16
Words for fractionals 16 (Decimals for display 77)
OK
run
 0.63818582086064415301550365944406770126515754397799768342106208158057548513945

 0.63818582086064415301550365944406770126515754397799768342106208158057548513989
 
which pushes the rounding error further down the line.

It seems both formulae represent the same value.