Synthesis of diethyloxalate from ethene
Conversion  1

Convert ethene to ethanol.
Ethene is mixed with steam and passed over a catalyst consisting of solid silicon dioxide coated with phosphoric(V) acid. The temperature used is 300 °C and the pressure is about 60 to 70 atmospheres (chemguide —
The mechanism for the acid catalysed hydration of ethene).
$$\ce{CH2=CH2 + H2O &lt;=&gt;[H3PO4] CH3CH2OH}$$

React the ethanol with oxalic acid to get diethyl oxalate.
$$\ce{(COOH)2 + 2C2H5OH -&gt;[CCl4,\Delta] (COOC2H5)2 + 2 H2O}$$
The details of this reaction is given on Organic Syntheses — Ethyl Oxalate and in the paper by Jewel and Butts [1].


Conversion 2
Convert ethene to oxalic acid by first converting to ethyne and then making oxalic acid from it. Use the oxalic acid to make diethyl oxalate by reacting it with absolute alcohol.
$$\ce{CH2=CH2 -&gt;[Br2][CCl4] Br-CH2-CH2-Br -&gt;[alc. KOH][\Delta] CH#CH -&gt;[alc. KMnO4] (COOH)2}$$
Reference

Jewel, P. W.; Butts, J. S. A Method for the Preparation of Diethyl Oxalate. J. Am. Chem. Soc. 1931, 53 (9), 3560–3561. DOI: 10.1021/ja01360a052.