Four digit numbers stored in a file are written in ASCII and separated by "Space", How do I read them as Integers. Example file: 53545153 49575150 56485654 53565257 52555756 51534850 56575356 56505055 55525453
Those look like 8 digit numbers.
To read a space separated number from a file simple use operator>> from a stream to an integer.
int value;
if (stream >> value) {
    // Successfully read a number.
}
If you want to read all the values from a file. You can use a loop:
int value;
while (stream >> value) {
    // Enter the body of the loop each time a number is read.
}
Note: Your usage of eof() is bad practice:
while (!infile.eof()) {
    // If you enter here the file may be open and readable
    // BUT there may be no data left in the file and thus the next
    // attempt to read will fail if there is no data.
    //
    // This happens because the last successful read will read up-to
    // but not past the EOF. So you have read all the data but not read
    // past the EOF so eof() will return false.
}
More Info
So how do we read 2 digit numbers from groups of 8 digit larger numbers that are space separated.
Well we want to make it work like standard stream readding so we still want to use the operator>> to read from the stream. But none of the built in types read two digit numbers. So we need to define our own class that will read a two digit number.
 struct TwoDigit
 {
     int    value;                  // store the result here
     operator int() {return value;} // Convert TwoDigit to integer
 };
 std::ostream& operator<<(std::ostream& str, TwoDigit const& data) {
     str << data.value; // You can do something more complicated
                        // for printing but its not the current question
                        // so I am just going to dump the value out.
 }
 std::istream& operator>>(std::istream& str, TwoDigit& data) {
     char c1 = 'X';
     char c2 = 'Y';
     if (str >> c1 >> c2) {
         // successfully read two characters from the stream.
         // Note >> automatically drops white space (space return etc)
         // so we don't need to worry about that.
         if (('0' <= c1 && c1 <= '9') && ('0' <= c2 && c2 <= '9')) {
              // We have all good data.
              // So let us update the vale.
              data.value = ((c1 - '0') * 10) + (c2 - '0');
         }
         else {
              // We have bad data read from the stream.
              // So lets mark the stream as bad;
              str.clear(std::ios::failbit);
         }
    }
    return str;
}
Now in your code you can simply read
 TwoDigit  data;
 if (stream >> data) {
      // Read a single two digit value correctly.
 }
 // or for a loop:
 while(stream >> data) {
      // Keep reading data from the stream.
      // Each read will consume two digits.
 }
 // or if you want to fill a vector from a stream.
 std::vector<TwoDigit> data(std::istream_iterator<TwoDigit>(stream),
                            std::istream_iterator<TwoDigit>());
 // You can even create a vector of int just as easily.
 // Because the TwoDigit has an `operator int()` to convert to int.
 std::vector<int>      data(std::istream_iterator<TwoDigit>(stream),
                            std::istream_iterator<TwoDigit>());