Execute a Jupyter notebook including inline markdown with nbconvert

The ExecutePreprocessor only looks at code cells, so your markdown cells are completely untouched. To do markdown processing, you need the Python Markdown preprocessor, as you have stated.

Unfortunately, the Python Markdown preprocessor system only executes the code in a live notebook, which it does by modifying the javascript involved with rendering cells. The modification stores the results of executing the code snippets in the cell metadata.

The PyMarkdownPreprocessor class (in pre_pymarkdown.py) was designed to be used with nbconvert operating on notebooks that had been rendered first in a live notebook setting. It processes markdown cells, replacing {{}} patterns with the values stored in the metadata.

In your situation, however, you don't have the live notebook metadata. I had a similar problem, and I solved it by writing my own execution preprocessor that also included logic to handle the markdown cells:

from nbconvert.preprocessors import ExecutePreprocessor, Preprocessor
import nbformat, nbconvert
from textwrap import dedent

class ExecuteCodeMarkdownPreprocessor(ExecutePreprocessor):

    def __init__(self, **kw):
        self.sections = {'default': True} # maps section ID to true or false
        self.EmptyCell = nbformat.v4.nbbase.new_raw_cell("")

        return super().__init__(**kw)

    def preprocess_cell(self, cell, resources, cell_index):
        """
        Executes a single code cell. See base.py for details.
        To execute all cells see :meth:`preprocess`.
        """

        if cell.cell_type not in ['code','markdown']:
            return cell, resources

        if cell.cell_type == 'code':
            # Do code stuff
            return self.preprocess_code_cell(cell, resources, cell_index)

        elif cell.cell_type == 'markdown':
            # Do markdown stuff
            return self.preprocess_markdown_cell(cell, resources, cell_index)
        else:
            # Don't do anything
            return cell, resources

    def preprocess_code_cell(self, cell, resources, cell_index):
        ''' Process code cell.
        '''
        outputs = self.run_cell(cell)
        cell.outputs = outputs

        if not self.allow_errors:
            for out in outputs:
                if out.output_type == 'error':
                    pattern = u"""\
                        An error occurred while executing the following cell:
                        ------------------
                        {cell.source}
                        ------------------
                        {out.ename}: {out.evalue}
                        """
                    msg = dedent(pattern).format(out=out, cell=cell)
                    raise nbconvert.preprocessors.execute.CellExecutionError(msg)

        return cell, resources

    def preprocess_markdown_cell(self, cell, resources, cell_index):
        # Find and execute snippets of code
        cell['metadata']['variables'] = {}
        for m in re.finditer("{{(.*?)}}", cell.source):
            # Execute code
            fakecell = nbformat.v4.nbbase.new_code_cell(m.group(1))
            fakecell, resources = self.preprocess_code_cell(fakecell, resources, cell_index)

            # Output found in cell.outputs
            # Put output in cell['metadata']['variables']
            for output in fakecell.outputs:
                html = self.convert_output_to_html(output)
                if html is not None:
                    cell['metadata']['variables'][fakecell.source] = html
                    break
        return cell, resources

    def convert_output_to_html(self, output):
        '''Convert IOpub output to HTML

        See https://github.com/ipython-contrib/IPython-notebook-extensions/blob/master/nbextensions/usability/python-markdown/main.js
        '''
        if output['output_type'] == 'error':
            text = '**' + output.ename + '**: ' + output.evalue; 
            return text
        elif output.output_type == 'execute_result' or output.output_type == 'display_data':
            data = output.data
            if 'text/latex' in data:
                html = data['text/latex']
                return html
            elif 'image/svg+xml' in data:
                # Not supported
                #var svg = ul['image/svg+xml'];
                #/* embed SVG in an <img> tag, still get eaten by sanitizer... */
                #svg = btoa(svg);
                #html = '<img src="data:image/svg+xml;base64,' + svg + '"/>';
                return None
            elif 'image/jpeg' in data:
                jpeg = data['image/jpeg']
                html = '<img src="data:image/jpeg;base64,' + jpeg + '"/>'
                return html
            elif 'image/png' in data:
                png = data['image/png']
                html = '<img src="data:image/png;base64,' + png + '"/>'
                return html
            elif 'text/markdown' in data:
                text = data['text/markdown']
                return text
            elif 'text/html' in data:
                html = data['text/html']
                return html
            elif 'text/plain' in data:
                text = data['text/plain']
                # Strip <p> and </p> tags
                # Strip quotes
                # html.match(/<p>([\s\S]*?)<\/p>/)[1]
                text = re.sub(r'<p>([\s\S]*?)<\/p>', r'\1', text)
                text = re.sub(r"'([\s\S]*?)'",r'\1', text)
                return text
            else:
            # Some tag we don't support
                return None
        else:
            return None

You can then process you notebook with logic similar to your posted code:

import nbformat
from nbconvert.preprocessors import ExecutePreprocessor
import ExecuteCodeMarkdownPreprocessor # from wherever you put it
import PyMarkdownPreprocessor # from pre_pymarkdown.py

with open('report.ipynb') as f:
    nb = nbformat.read(f, as_version=4)
    ep = ExecuteCodeMarkdownPreprocessor(timeout=600, kernel_name='python3')
    ep.preprocess(nb, {})
    pymk = PyMarkdownPreprocessor()
    pymk.preprocess(nb, {})

with open('report_executed.ipynb', 'wt') as f:
    nbformat.write(nb, f)

Note that by including the Python Markdown preprocessing, your resultant notebook file will no longer have the {{}} syntax in the markdown cells - the markdown will have static content. If the recipient of the resultant notebook changes the code and executes again, the markdown will not be updated. However, if you are exporting to a different format (such as HTML), then you do want to replace the {{}} syntax with static content.