Start by preparing the sugar syrup; combine the caster sugar and water in a small saucepan. Bring to a simmer over a medium heat, stirring as you do to dissolve the sugar. Once dissolved, continue to simmer for 2-3 minutes to thicken the syrup a little. Remove from the heat and allow to cool to one side.
Meanwhile, purée the raspberries by mashing them in a bowl using a potato masher; alternatively, blend in a food processor until smooth. Press the purée through a fine sieve sat on top of a bowl to collect the purée.
To make the cocktails
Half-fill a shaker with ice cubes. Add 50ml of vodka, 25ml of sugar syrup and 50ml of raspberry purée to the shaker. Shake well for 30-45 seconds. Strain into a martini glass and garnish with a sprig of mint and a couple of raspberries on the rim of the glass. Repeat until you have 4 martinis.