How to understand C++ std::setw 's inconsisten

Question

Given the following code:

/*Formatting Output 
**Goal: practice using cout to format output to console
**Print the variables in three columns:
**Ints, Floats, Doubles
*/

#include <iostream>
#include <iomanip>

using namespace std;

int main()
{
    int a = 45;
    float b = 45.323;
    double c = 45.5468;
    int aa = a + 9;
    float bb = b + 9;
    double cc = c + 9;
    int aaa = aa + 9;
    float bbb = bb + 9;
    double ccc = cc + 9;

    // 1st attempt :>

    cout << "\n\n\n" << "// 1st attempt :>" << "\n";
    cout << "12345678901234567890123456789012345678901234567890" << "\n";
    cout << "Ints" << setw(15) << "Floats" << setw(15) << "Doubles" << "\n";
    cout << a << setw(15) << b << setw(15) << c << "\n";
    cout << aa << setw(15) << bb << setw(15) << cc << "\n";
    cout << aaa << setw(15) << bbb << setw(15) << ccc << "\n";


    // 2nd attempt :>

    cout << "\n\n\n" << "// 2nd attempt :>" << "\n";
    cout << "12345678901234567890123456789012345678901234567890" << "\n";
    cout << std::left << std::setfill(' ') << std::setw(15)  << "Ints" << setw(15) << "Floats" << setw(15) << "Doubles" << "\n";
    cout << a << setw(15) << b << setw(15) << c << "\n";
    cout << std::left << std::setfill(' ') << setw(15) << aa << setw(15) << bb << setw(15) << cc << "\n";
    cout << aaa << setw(15) << bbb << setw(15) << ccc << "\n";

    // 3rd attempt :>

    cout << "\n\n\n" << "// 3rd attempt :>" << "\n";
    cout << "12345678901234567890123456789012345678901234567890" << "\n";
    cout << std::left << std::setfill(' ') << std::setw(15) << "Ints" << setw(15) << "Floats" << setw(15) << "Doubles" << "\n";
    cout << std::left << std::setfill(' ') << std::setw(15) << a << setw(15) << b << setw(15) << c << "\n";
    cout << std::left << std::setfill(' ') << std::setw(15) << aa << setw(15) << bb << setw(15) << cc << "\n";
    cout << std::left << std::setfill(' ') << std::setw(15) << aaa << setw(15) << bbb << setw(15) << ccc << "\n";
    cout << "12345678901234567890123456789012345678901234567890" << "\n";
    cout << std::right << std::setfill(' ') << std::setw(15) << "Ints" << setw(15) << "Floats" << setw(15) << "Doubles" << "\n";
    cout << std::right << std::setfill(' ') << std::setw(15) << a << setw(15) << b << setw(15) << c << "\n";
    cout << std::right << std::setfill(' ') << std::setw(15) << aa << setw(15) << bb << setw(15) << cc << "\n";
    cout << std::right << std::setfill(' ') << std::setw(15) << aaa << setw(15) << bbb << setw(15) << ccc << "\n";

    return 0;
}
// https://repl.it/@Tredekka/Cpp-Understanding-stdsetw

... I get the following output:

gcc version 4.6.3

// 1st attempt :>
12345678901234567890123456789012345678901234567890
Ints         Floats        Doubles
45         45.323        45.5468
54         54.323        54.5468
63         63.323        63.5468



// 2nd attempt :>
12345678901234567890123456789012345678901234567890
Ints           Floats         Doubles        
4545.323         45.5468        
54             54.323         54.5468        
6363.323         63.5468        



// 3rd attempt :>
12345678901234567890123456789012345678901234567890
Ints           Floats         Doubles        
45             45.323         45.5468        
54             54.323         54.5468        
63             63.323         63.5468        
12345678901234567890123456789012345678901234567890
           Ints         Floats        Doubles
             45         45.323        45.5468
             54         54.323        54.5468
             63         63.323        63.5468

... note: I was intentionally "inconsistent" with the code, "because" I'm trying to understand the behavior of the <iomanip> && std::setw() code.

If you look at the output from the 1st attempt, you'll notice that the header row "string" output is offset from the data rows "numerical" output... and while it's "mostly" accomplishing the purpose of aligning things in columns, it's both not accurate and not consistent.

In the 2nd attempt, you'll see that I've discovered that if I prepend my row output with:

<< std::left << std::setfill(' ') << setw(15)

... then I get the row to look correctly (as seen in the header & 2nd data row) ... but now you'll notice that the 1st & 3rd data rows are very wrong:

4545.323         45.5468        
...       
6363.323         63.5468      

... how does "using/executing" ...

<< std::left << std::setfill(' ') << setw(15)

... affect "future" executions of setw()?

For completeness' sake, I've shown in the 3rd Attempt that it's possible to correctly & accurately align columns of data (either left or right) using <iomanip> && std::setw() ... but why the inconsistencies?

(@WhozCraig's answer helped me get to where I am, but did not delve deep enough to help me understand either: (a) why it 'pseudo' works || (b) why after you make it work correctly the 'first' time, it then breaks the 'pseudo' functionality.)