How to find the second order Taylor of F(x, y) = y^3 ? 2x^3 + 2y ? 1?

Questions
1

Verify that the equation F (x, y) = 0 near the point (x0, y0) = 1 to
unloading is in the form y = ? (x), and give the second order Taylor Approach
for ? around x0 = 1.

2

This comes across as a raw homework problem, which is not appropriate for this forum.

At least translate it into Wolfram Language. Basic tutorials are at