const to Non-const Conversion in C++

The actual code to cast away the const-ness of your pointer would be:

BoxT<T> * nonConstObj = const_cast<BoxT<T> *>(constObj);

But note that this really is cheating. A better solution would either be to figure out why you want to modify a const object, and redesign your code so you don't have to.... or remove the const declaration from your vector, if it turns out you don't really want those items to be read-only after all.

You can assign a const object to a non-const object just fine. Because you're copying and thus creating a new object, constness is not violated.

Like so:

int main() {
   const int a = 3;
   int b = a;
}

It's different if you want to obtain a pointer or reference to the original, const object:

int main() {
   const int a = 3;
   int& b = a;       // or int* b = &a;
}

//  error: invalid initialization of reference of type 'int&' from
//         expression of type 'const int'

You can use const_cast to hack around the type safety if you really must, but recall that you're doing exactly that: getting rid of the type safety. It's still undefined to modify a through b in the below example:

int main() {
   const int a = 3;
   int& b = const_cast<int&>(a);

   b = 3;
}

Although it compiles without errors, anything can happen including opening a black hole or transferring all your hard-earned savings into my bank account.

If you have arrived at what you think is a requirement to do this, I'd urgently revisit your design because something is very wrong with it.

Changing a constant type will lead to an Undefined Behavior.

However, if you have an originally non-const object which is pointed to by a pointer-to-const or referenced by a reference-to-const then you can use const_cast to get rid of that const-ness.

Casting away constness is considered evil and should not be avoided. You should consider changing the type of the pointers you use in vector to non-const if you want to modify the data through it.