İ’m solving an SOCP problem, MOSEK or sdpt3 and even sedumi are giving same estimate , will Gurobi give the same , İ dont have it installed

Probably the same optimal objective function, but possible different argmin (or argmax) if not unique.

If you show your code and the Mosek solution log, the Mosek people who read this forum can comment on the apparent reliability of the solution.

There were apparent bugs in the CVX-Gurobi interface (sometimes resulting in correct solutions) - I don’t know whether they have been resolved. I doubt you will do better on continuous SOCPs using Gurobi under CVX than Mosek. However, for Mixed-Integer SOCP, that might not necessarily be so.

Here is another random thought.

Assume you have a number of optimizers. Also assume that (almost) all the optimizers produce a solution you like and that perhaps fairly quickly. Then most likely you a great model.

On the other hand if only one optimizer solves your model satisfactorily, then most likely there are something odd about your model. And maybe it was just random luck that the optimizer could solve it.