3d array as double pointer, freeing memory after usage - c++

Question

First off, let me say that everything works like a charm, but the memory deallocation. Maybe it's pure coincidence that I do not have any problems and my basic understanding is wrong.
Also, please refrain from telling me "Use std::vector instead" or the like, as I want to learn and understand the basics first!
Now to the code:
class Test
{
public:
Test(const unsigned int xDim, const unsigned int yDim, const unsigned int zDim);
~Test();
private:
unsigned int xDim, yDim, zDim;
TestStructure **testStructure;
void init();
int to1D(int x, int y, int z) { return x + (y * xDim) + (z * xDim * yDim); }
}
cpp:
Test::Test(const unsigned int xDim, const unsigned int yDim, const unsigned int zDim)
{
this->xDim = xDim;
this->yDim = yDim;
this->zDim = zDim;
this->testStructure = new TestStructure *[xDim * yDim * zDim];
init();
}
void Test::init()
{
for(int x = 0; x < xDim; x++)
for(int y = 0; y < yDim; y++)
for(int z = 0; z < zDim; z++)
{
this->testStructure[to1D(x, y, z)] = new TestStructure(
x - xDim / 2,
y - yDim / 2,
z - zDim / 2);
...
}
Now for the destructor I tried two ways:
Test::~Test()
{
for(int x = 0; x < xDim; x++)
for(int y = 0; y < yDim; y++)
for(int z = 0; z < zDim; z++) {
free(this->testStructure[to1D(x, y, z)]);
}
free(this->testStructure);
}
and
Test::~Test()
{
for(int a = 0; a < xDim * yDim * zDim; a++) {
free(this->testStructure[a]);
}
free(this->testStructure);
}
I am pretty sure the second is like the first, but In both cases I get:
==3854==ERROR: AddressSanitizer: alloc-dealloc-mismatch (operator new vs free) on 0x62100008e900
Where are my mistakes? Throw them at my face and let me learn!
edit: Basic mistake: use delete (for new) instead of free (for malloc).
Replacing the frees above with deletes leads to:
==4076==ERROR: AddressSanitizer: new-delete-type-mismatch on 0x60600002c300 in thread T0:
edit2:
Pardon me, with delete[] for the array part it leads to:
==4138==ERROR: AddressSanitizer: heap-buffer-overflow on address 0x62100008e8f8 at pc 0x000000480b3d bp 0x7ffc5bcbc0f0 sp 0x7ffc5bcbc0e0
edit3/SOLUTION: Did it the wrong way. This seems to work:
Test::~Test()
{
for(int a = 0; a < xDim * yDim * zDim; a++) {
delete(this->testStructure[a]);
}
delete[] this->testStructure;
}
Big thanks #SomeProgrammerDude